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The sum of square of 2 number is 1972 and the difference of their square is 620. Find the number ?
- a)33,26
- b)34,25
- c)36,26
- d)38,28
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The sum of square of 2 number is 1972 and the difference of their squa...
X2 + y2 = 1972
X2 – y2 = 620
Solve this
2x2 = 2592
x = 1296
x = 36
y2 = 1972 – 1296
y2 = 676
y = 26
X2 – y2 = 620
Solve this
2x2 = 2592
x = 1296
x = 36
y2 = 1972 – 1296
y2 = 676
y = 26
Most Upvoted Answer
The sum of square of 2 number is 1972 and the difference of their squa...
The correct answer is C)36,26
Let suppose that two numbers are A and B.
then according to given condition
sum of the squares of these two number is 1972. so
A² + B² =1972. (equation 1)
and difference of the squares of these number is 620 .so
A² - B² =620. . . (equation 2)
by adding equation 1 and 2
A² + B² =1972
+ A² - B² =690
----------------
2A² + 0 = 2592
2A² =2592
A²= 2592/2
A² =1296
And Taking under root(√) both sides
√A² =√1296
A = 36
by putting the values Of A in equation 1 (A=36)
equation 1
A² + B² = 1972
we know that A=36. so
(36)² + B² =1972
1296 + B² = 1972
B² =1972-1296
B² = 676
taking under root(√) both sides
√B² =√676
B = 26 A=36
---------------------------
For checking the answers A=36 and B=26
according to given Condition
A² + B² = 1972
by putting values
36² + 26² = 1972
1296 + 676 = 1972
1972 = 1972 (Proved the condition)
2nd given condition
A² - B² = 620
by putting values A=36 and B=26
36² -26² =620
1296 - 676 =620
620=620. (Proved the 2nd condition is also correct )
So the Answer is
(36,26)
Let suppose that two numbers are A and B.
then according to given condition
sum of the squares of these two number is 1972. so
A² + B² =1972. (equation 1)
and difference of the squares of these number is 620 .so
A² - B² =620. . . (equation 2)
by adding equation 1 and 2
A² + B² =1972
+ A² - B² =690
----------------
2A² + 0 = 2592
2A² =2592
A²= 2592/2
A² =1296
And Taking under root(√) both sides
√A² =√1296
A = 36
by putting the values Of A in equation 1 (A=36)
equation 1
A² + B² = 1972
we know that A=36. so
(36)² + B² =1972
1296 + B² = 1972
B² =1972-1296
B² = 676
taking under root(√) both sides
√B² =√676
B = 26 A=36
---------------------------
For checking the answers A=36 and B=26
according to given Condition
A² + B² = 1972
by putting values
36² + 26² = 1972
1296 + 676 = 1972
1972 = 1972 (Proved the condition)
2nd given condition
A² - B² = 620
by putting values A=36 and B=26
36² -26² =620
1296 - 676 =620
620=620. (Proved the 2nd condition is also correct )
So the Answer is
(36,26)
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Community Answer
The sum of square of 2 number is 1972 and the difference of their squa...
Problem Analysis:
Let's assume the two numbers as x and y. According to the problem, we have two equations:
1) x^2 + y^2 = 1972
2) x^2 - y^2 = 620
Solution:
To find the numbers, we can solve the equations simultaneously.
Step 1: Simplify the second equation
x^2 - y^2 = (x + y)(x - y) = 620
Step 2: Factorize 620
620 = 2 * 2 * 5 * 31
Step 3: Write down all possible combinations of factors of 620
(x + y)(x - y) = 620
Possible combinations are:
(i) x + y = 620 and x - y = 1
(ii) x + y = 310 and x - y = 2
(iii) x + y = 155 and x - y = 4
(iv) x + y = 124 and x - y = 5
(v) x + y = 62 and x - y = 10
(vi) x + y = 31 and x - y = 20
Step 4: Solve each combination to find x and y
(i) Adding equations (i) and (ii)
2x = 621
x = 310.5 - Not possible as x should be an integer
(ii) Adding equations (ii) and (iii)
2x = 314
x = 157
Substituting x = 157 in equation (ii)
157 + y = 310
y = 310 - 157 = 153
(iii) Adding equations (iii) and (iv)
2x = 159
x = 79.5 - Not possible as x should be an integer
(iv) Adding equations (iv) and (v)
2x = 129
x = 64.5 - Not possible as x should be an integer
(v) Adding equations (v) and (vi)
2x = 92
x = 46
Substituting x = 46 in equation (v)
46 + y = 72
y = 72 - 46 = 26
Step 5: Check if the values satisfy the first equation
x^2 + y^2 = 1972
For x = 157 and y = 153:
157^2 + 153^2 = 24649 + 23409 = 48058 ≠ 1972
For x = 46 and y = 26:
46^2 + 26^2 = 2116 + 676 = 2792 ≠ 1972
Therefore, the correct answer is option 'C' 36, 26.
Let's assume the two numbers as x and y. According to the problem, we have two equations:
1) x^2 + y^2 = 1972
2) x^2 - y^2 = 620
Solution:
To find the numbers, we can solve the equations simultaneously.
Step 1: Simplify the second equation
x^2 - y^2 = (x + y)(x - y) = 620
Step 2: Factorize 620
620 = 2 * 2 * 5 * 31
Step 3: Write down all possible combinations of factors of 620
(x + y)(x - y) = 620
Possible combinations are:
(i) x + y = 620 and x - y = 1
(ii) x + y = 310 and x - y = 2
(iii) x + y = 155 and x - y = 4
(iv) x + y = 124 and x - y = 5
(v) x + y = 62 and x - y = 10
(vi) x + y = 31 and x - y = 20
Step 4: Solve each combination to find x and y
(i) Adding equations (i) and (ii)
2x = 621
x = 310.5 - Not possible as x should be an integer
(ii) Adding equations (ii) and (iii)
2x = 314
x = 157
Substituting x = 157 in equation (ii)
157 + y = 310
y = 310 - 157 = 153
(iii) Adding equations (iii) and (iv)
2x = 159
x = 79.5 - Not possible as x should be an integer
(iv) Adding equations (iv) and (v)
2x = 129
x = 64.5 - Not possible as x should be an integer
(v) Adding equations (v) and (vi)
2x = 92
x = 46
Substituting x = 46 in equation (v)
46 + y = 72
y = 72 - 46 = 26
Step 5: Check if the values satisfy the first equation
x^2 + y^2 = 1972
For x = 157 and y = 153:
157^2 + 153^2 = 24649 + 23409 = 48058 ≠ 1972
For x = 46 and y = 26:
46^2 + 26^2 = 2116 + 676 = 2792 ≠ 1972
Therefore, the correct answer is option 'C' 36, 26.
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The sum of square of 2 number is 1972 and the difference of their square is 620. Find the number ?a)33,26b)34,25c)36,26d)38,28Correct answer is option 'C'. Can you explain this answer?
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The sum of square of 2 number is 1972 and the difference of their square is 620. Find the number ?a)33,26b)34,25c)36,26d)38,28Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The sum of square of 2 number is 1972 and the difference of their square is 620. Find the number ?a)33,26b)34,25c)36,26d)38,28Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of square of 2 number is 1972 and the difference of their square is 620. Find the number ?a)33,26b)34,25c)36,26d)38,28Correct answer is option 'C'. Can you explain this answer?.
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