Math, asked by krati37, 1 year ago

If 3x - 5y = 9 and xy = 24 , find the value of 9x^2 + 25y^2​

Answers

Answered by priyabachala
3

3x-5y= 9 ...............[1] and x-y = 24

squraing on both sides

9x²+25y²-2(3x)(5y) = 81

9x²+25y²-30xy = 81

9x² +25y² = 81+30(24) = 81+720

= 801

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krati37: thanks
priyabachala: it's ok
priyabachala: Pls mark as brainlist
Answered by Anonymous
15

3x - 5y = 9 \\  \\ to \: find \\  \\  =  \geqslant 9 {x}^{2}  + 25 {y}^{2}  \\  \\  =  \geqslant given \: xy = 24 \\  \\  =  \geqslant now \: squaring \: both \: sides \\  \\  =  \geqslant (3x - 5y) {}^{2}  =  {9}^{2}  \\  \\  =  \geqslant 9 {x}^{2}  + 25 {y}^{2}  - 2 \times 3x \times 5y = 81 \\  \\  =  \geqslant 9 {x}^{2}  + 25 {y}^{2}  - 30xy = 81 \\  \\  =  \geqslant 9 {x}^{2}  + 25 {y}^{2}  - 30 \times 24 = 81 \\  \\  =  \geqslant 9 {x}^{2}  + 25 {y}^{2}  - 720 = 81 \\  \\  =  \geqslant 9 {x}^{2}  + 25 {y}^{2}  = 720 + 81 = 801

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