Question

$\sqrt{3 { x}^{2} - 7x - 30 } - \sqrt{2 {x}^{2} - 7x - 5 } = x - 5$
prove the following equation

Answer 1

Final Answer : 5,6


Steps :
1) Let a = first term of LHS
b = second term of LHS.
2) Now,
we know that
This is bit trickiest step.
BY OBSERVING,

a^2 - b^2 = x^2-25


3) Now,
a-b = x - 5. ( given)
From here. and 2). we cancelled x -5 , as x = 5 can also be solution.
Using 2) we get a = x, b = 5 .
These two both gives x = 6 .

For Calculation see pic.