Question

solve √(3x²-7x-30)+√(2x²-7x-5)=x+5​

Answer 1

HELLO DEAR,

GIVEN:- √(3x²-7x-30)+√(2x²-7x-5)= x+5

now, √(3x² - 7x - 30) = (x + 5) - √(2x² - 7x - 5)

on squaring both side,

=> (3x² - 7x - 30) = [(x + 5)² + {√(2x² - 7x - 5)}² - 2(x + 5)√(2x² - 7x - 5)]

=> (3x² - 7x - 30) = (x² + 25 + 10x) + (2x² - 7x - 5) - 2(x + 5)√(2x² - 7x - 5)

=> 3x² - 3x² - 7x - 10x + 7x - 30 - 25 + 5 = -2(x + 5)√(2x² - 7x - 5)

=> -10x - 50 = -2(x + 5)√(2x² - 7x - 5)

=> -10(x + 5) = -2(x + 5)√(2x² - 7x - 5)

=> 5 = √(2x² - 7x - 5)

=> 25 = 2x² - 7x - 5

=> 2x² - 7x - 30 = 0

=> 2x² - 12x + 5x - 30 = 0

=> 2x(x - 6) + 5(x - 6) = 0

=> (2x + 5)(x - 6)

=> x = -5/2 & x = 6

I HOPE IT'S HELP YOU DEAR,

I HOPE IT'S HELP YOU DEAR,THANKS