Question

if
$9 {x}^{2} + 25 {y}^{2} = 181 \:$
and xy = -6 then ( 3x + 5y ) is equal to?
​

Answer 1

$\large{\underline{\bf{Given:-}}}$

❒ 9x² + 25y² = 181

❒ xy = -6

$\large{\underline{\bf{Find:-}}}$

❒ Value of (3x + 5y)

$\large{\underline{\bf{Solution:-}}}$

we, have

⇁9x² + 25y² = 181 $\qquad$ 〘Given〙

Taking L.H.S

↦9x² + 25y² = (3x)² + (5y)²

➠(3x + 5y)²

$\sf\bigstar using \: {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \bigstar$

➠(3x)² + 2(3x)(5y) + (5y)²

➠9x² + 30xy + 25y²

$\sf\bigstar Rearranging \: the \: term\bigstar$

➠9x² + 25y² + 30xy

$\sf\bigstar using \: 9x^{2} + 25 y^{2} = 181\bigstar$

➠181 + 30xy

$\sf\bigstar now, \: using \:xy = - 6\bigstar$

➠181 + 30(-6)

➠181 + (-180)

➠181 - 180

➠1

⇨3x + 5y = 1 $\purple\bigstar$

Hence, answer is 1