Question

if x is real and setisfies x+2>✓x+4 then​

Answer 1

Given:

A inequality x+2 > √x+4 .

To Find:

The range of values of 'x'.

Concept Used:

We will square both sides and then further simplify it.

Solution:

We have,

=> x+2 > √x + 4 .

Squaring both sides,

=> (x+2)² > (√x+4)².

=> (x+2)²> x+4 .

=> x²+4 + 4x > x + 4 .

=> x² +(4x - x )+4 -4 > 0

=> x² + 3x > 0 .

=> x(x+3) > 0

=> x > 0 (1) or x+3>0 (2)

.°. From (1),

=> x > 0 .

.°. $\sf{x\epsilon (0,\infty)}$

From (2),

=> x+3>0

=> x> -3

.°. $\sf{x\epsilon (-3,-\infty)}$

.°. x E (-3,-∞) U (0,∞).