Question

If 3x+5y=6 and x y = -2 ,find the value of 9x^2+25y^2

Answer 1

$given - \: 3x + 5y = 6 \: and \: xy = -2 \\ \\ = > 3x + 5y =6 \\ \: \: \: \: \: \: \: \: \: \: \: \: squaring \: both \: sides - - - \\ \\ = > (3x + 5y) {}^{2} = (6) {}^{2} \\ = > (3x) {}^{2} + (5y) {}^{2} + 2xy = 36 \\ = > 9x {}^{2} + 25y {}^{2} + 2( - 2) = 36 \\ = > 9x {}^{2} + 25y {}^{2} - 4 = 36 \\ = > 9x {}^{2} + 25y {}^{2} = 36 + 4 \\ = > 9x {}^{2} + 25y {}^{2} = 40 \\ \\ \\ please \: mark \: it \: as \: brainliest.$

Answer 2

Hope you like my process
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given
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=> xy = -2

=> 3x + 5y = 6

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Now
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=> 3x + 5y = 6

Squaring both sides.
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=> (3x +5y)² = 6²

=> (3x)² + (5y)² + 2(3x)(5y)=36

=> 9x² +25y² + 30xy =36

=> 9x² +25y² = 36 -30xy = 36 -30(-2)

=> 9x² +25y² = 36 + 60 = 96

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Hence

=> 9x² +25y² = 96

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