Question

If 3x + 5y = 11 and xy = 2, find the value of
$9 {x}^{2} + 25{y}^{2}$
​

Answer 1

Given:

3x + 5y=11

xy=2

as a^2 + b^2 could be written as (a+b)^2 - 2ab

In the same manner,

9x^2 + 25y^2 could be written as

(3x+5y)^2 - 2(3x)(5y)

(3x + 5y)^2 - 30xy

now, substitute the given values.,

(11)^2 - 30 (2)

= 121 - 60

= 61.

so here,

9x^2 + 25y^2 = 61