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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?
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...
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
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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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Question Description
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