Question

Find the value of 9x^2 + 25y^2 if 3x + 5y = 8 and xy = 0.5.​

Answer 1

Answer:

49

Step-by-step explanation:

we can say that

$9 {x}^{2} + 25 {y}^{2} = {(3x)}^{2} + {(5y)}^{2}$

as 3x+5y=8

if we square both side

${(3x + 5y)}^{2} = {(8)}^{2} \\ {(3x)}^{2} + {(5y)}^{2} + 30xy = 64 \\ now \: keeping \: the \: value \: \\ of\: xy \:$

${9x}^{2} + {25y}^{2} + 30 \times 0.5 = 64 \\ {9x}^{2} + {25y}^{2} = 64 - 15 \\ {9x}^{2} + {25y}^{2} = 49$

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Answer 2

Step-by-step explanation:

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