The sum of two numbers is 15 and the sum of their square is 113 the numbers are:
Soln Date / Update:-22-Jul-2025 06:11PM
Solution:-
Exercise - 2 (A) Q-32.
The sum of two numbers is 15 and the sum of their square is 113 the numbers are:
(A) 4, 11 (B) 5, 10
(C) 6, 9 (D) 7, 8
Soln:-
Let the numbers x and y
Now, Sum of numbers = 15
x + y = 15 ----------(i)
Now again sum of their square = 113
x2 + y2 = 113
(x + y)2 - 2xy = 113
(15)2 - 2xy = 113
225 - 2xy = 113
225 - 113 = 2xy
112 = 2xy
xy = 112 / 2
xy = 56 -------------(ii)
Generate qudratic equation From Eq(i) and Eq(ii)
Or x2 - 15x + 56 = 0
Or x2 - 8x - 7x + 56 = 0
Or x ( x - 8) - 7 ( x - 8 ) = 0
( x - 8 ) ( x - 7 ) = 0
x - 8 = 0 x- 7 = 0
x = 8 x = 7
Putting the value of x in equation (i)
x + y = 15 x + y = 15
8 + y = 15 7 + y = 15
y = 15 -8 y = 15 - 7
y = 7 y = 8
Hence
x = 7, y = 8
x = 9, y = 7 Ans.
