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