Question

Find the value of 3x + 5y, if 9x^2 + 25y^2 = 181 and xy = -6​

Answer 1

$\tt\red{Question}$

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

$\tt{ Answer= \green{1}}$

Solution:

Given that,

⁣      9x²+25x²=181⁣        (I)

⁣      XY = -6⁣           ⁣   (ii)

Find :- 3x+5y

${\boxed{\sf{by\ using\ identity \red{(a+b)²= a²+b²+2ab}}}}$

$\tt{(3x+5y)²= 9x²+25y²+2 \times 3x \times.5y}$

$\tt{(3x+5y)²= 9x²+25y²+30xy ⁣       (iii)}$

now putting the value of (I) and (ii) in equation (iii)

$\tt{ → (3x+5y)²= 181+30×(-6)}$

$\tt{ → (3x+5y)²= 181-180 }$

$\tt{ → (3x+5y)²= 1}$

$\tt{ → (3x+5y)= \sqrt{1} }$

$\tt{→(3x+5y)= \sqrt{1 \times 1}}$

$\tt{→(3x+5y)= 1}$

so the value of 3x+5y= 1

$\tt{ }$