Question

Prove that the following equations has no solutions:
√(x-4) = -5​

Answer 1

To prove:

$\sf{\sqrt{x-4}=-5 \ has \ no \ solution.}$

Proof:

$\sf{\leadsto{\sqrt{x-4}=-5...(1)}}$

$\sf{On \ squaring \ both \ sides, \ we \ get}$

$\sf{\leadsto{x-4=25}}$

$\sf{\leadsto{x=25+4}}$

$\sf{\leadsto{x=29}}$

$\sf{In \ equation (1)}$

$\sf{L.H.S.=\sqrt{x-4}}$

$\sf{=\sqrt{29-4}}$

$\sf{=\sqrt{25}}$

$\sf{=5}$

$\sf{But, \ R.H.S.=-5}$

$\sf{Since, \ L.H.S.\neq \ R.H.S.}$

$\sf\purple{\tt{Equation \ has \ no \ solution.}}$