Question

4x +5y =18 , xy = 4 then 16x^2 + 25y^2​

Answer 1

Step-by-step explanation:

Given:- 4x + 5y = 18....................(1)

xy = 4 ......................(2)

therefore, 16x^2 + 25y^2

= (4x)^2 + (5y)^2.

= (4x + 5y)^2 -- 2 × 4x × 5y .

[ since, a^2 + b^2 = (a + b)^2 - 2ab]

= (18)^2 - 40xy. [ by (1) ]

= 324 - 40 × 4. [ by (2) ]

= 324 - 160

= 164.

hence, 16x^2 + 25y^2 = 164.