Let x be a real number such that x 0 Prove that x 14x 1Sol

Let x be a real number such that x > 0. Prove that x + 1/4x 1.

Solution

If the question is : Prove x+ (1/4)x >= 1 and given x > 0

x( 1 +1/4) > = 1

x*5/4 > = 1

5x >= 4

x > = 4/5 ----> [ 4/5 , infinity)

which is true as x is already >0

So,   x+ (1/4)x >= 1 holds true