Question

If 5x – 3y = 9 and xy = -7, then the value of 25x² + 9y² is



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Answer 1

Answer:

25x² + 9y² = - 129

Option A (-129) is correct.

Step-by-step explanation:

using formula,

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

5x – 3y = 9

squaring both side

${(5x - 3y)}^{2} = {9}^{2} \\ {(5x)}^{2}- 2(5x)(3y) + {(3y)}^{2} = 81 \\ 25{x}^{2} - 30xy + 9 {y}^{2} = 81 \\ 25{x}^{2}+ 9 {y}^{2} = 81 + 30xy \\ 25{x}^{2}+ 9 {y}^{2} = 81 + 30( - 7) \\ 25{x}^{2}+ 9 {y}^{2} = 81 - 210 \\ 25{x}^{2}+ 9 {y}^{2} = - 129$