If 9 x 2-25 y 2-181 and xy -6 - Find the value of 3 x -5 yA- 3B- 2C- -2D- -1

The correct option is D 1 9x^2 + 25y^2 = 181 (3x)^2 + (5y)^2 = 181 ⇒(3x)^2 + (5y)^2 + 30xy 30xy = 181 ⇒(3x)^2 + (5y)^2 + 2(5x)(6y) = 181 + 30xy ⇒(3x + 5y)^2 ...

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Byju's Answer

Standard IX

Mathematics

Identity (x+y)^2

If 9 x 2+25 y...

Question

If ${9 x}^{2} + {25 y}^{2} = 181$ and xy = - 6. Find the value of 3x + 5y.

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Solution

The correct option is C
-1

${9 x}^{2} + {25 y}^{2} = 181$

$(3 x)^{2} + {(5 y)}^{2} = 181$

$\Rightarrow {(3 x)}^{2} + {(5 y)}^{2} + 30 x y - 30 x y = 181$

$\Rightarrow {(3 x)}^{2} + {(5 y)}^{2} + 2 (5 x) (6 y) = 181 + 30 x y$

$\Rightarrow {(3 x + 5 y)}^{2} = 181 + 30 (- 6) = 181 - 180$

$\Rightarrow {(3 x + 5 y)}^{2} = 1$

$\Rightarrow 3 x + 5 y = \pm$ 1

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If 9x2+25y2=181 and xy = - 6. Find the value of 3x + 5y.

The correct option is C -1 9x2+25y2=181 (3x)2+(5y)2=181 ⇒(3x)2+(5y)2+30xy−30xy=181 ⇒(3x)2+(5y)2+2(5x)(6y)=181+30xy ⇒(3x+5y)2=181+30(−6)=181−180 ⇒(3x+5y)2=1 ⇒3x+5y=±1

If ${9 x}^{2} + {25 y}^{2} = 181$ and xy = - 6. Find the value of 3x + 5y.