Question

If 9X2 +25y2 = 181 and xy = - 6 , find the value of 3x + 5y.

Answer 1

Solution is attached below

Answer 2

Step-by-step explanation:

Given:−

❒ 9x² + 25y² = 181

❒ xy = -6

Find:−

❒ Value of (3x + 5y)

Solution:−

we, have

⇁9x² + 25y² = 181 〘Given〙

Taking L.H.S

↦9x² + 25y² = (3x)² + (5y)²

➠(3x + 5y)²

★using {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}

➠(3x)² + 2(3x)(5y) + (5y)²

➠9x² + 30xy + 25y²

★Rearranging The Term★

➠9x² + 25y² + 30xy

★ using 9x^{2} + 25 y^{2} = 181

➠181 + 30xy

★now, using xy = - 6

➠181 + 30(-6)

➠181 + (-180)

➠181 - 180

➠1

⇨3x + 5y = 1

Hence, answer is 1