Question

sqrt(5 - x) > x + 1
What is the answer? ​

Answer 1

Answer:

Given:

√(5-x) > (x+1).

Squaring on both sides, we get,

(5-x) > (x+1)².

That is,

(5-x) > x² + 1 + 2x.

Transposing (5-x) to the other side,

0 > x² + 1 + 2x - 5 + x.

0 > x² + 3x - 4.

Solving the quadratic equation, we get,

0 > x² + 4x - x - 4.

0 > x(x+4) -1(x+4).

0 > (x+4)(x-1).

So,

0 > (x+4) ,OR, 0 > (x-1).

-4 > x ,OR, 1 > x.

Therefore,

→ X can be lesser than (-4), or,

→ X can be lesser than 1.