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?

Question

Answer

X² + y² = 1972
X² – y² = 620
Solve this
2x² = 2592
x = 1296
x = 36
y² = 1972 – 1296
y² = 676
y = 26

Answer

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)

Answer

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.

Similar Quant Doubts

ABCD is a square drawn inside a square PTRS of sides 4 cm by joining midpoints of the sides PR, PT, TS, SR. Another square is drawn inside ABCD similarly. This process is repeated infinite number of times. Find the sum of all the squares.

Sum of squares of two numbers is 145. If square root of one number is 3, find the other number.

Find the least square number (perfect squar e) which is exactly divisible by each of the numbers 6, 9, 12

Sum of squares of two numbers is 145. If square root of one number is 3, find the other number.

Sum of squares of two numbers is 145. If square root of one number is 3, find the other number.

Top Courses for Quant

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company