Inequality

Question

How to solve ?   k>k3 , if k is non negative integer

Groo · Answer

if k>0
k^3-k<0
k(k^2-1)<0
k=0, k=1,k=-1
Interval answer: (-R;-1) and (0;1)
as k is non negative, final answer is (0;1)

ak23456 · Answer

what will be for k<0? i saw in another post ths solution... If k>0, 1-k^2>0....k^2<1...-11...k<-1 how for k^2>1 , k < -1 ?

sujoykrdatta · Answer

Method 1 : Think of the number line and the main 4 regions: #a) x < -1 #b) -1 < x < 0 #c) 0 < x < 1 #d) x > 1 Try a number from each of these regions to check the inequality x > x^3 For #a) x = -2: -2 > -8 --- satisfies For #b) x = -1/2: -1/2 > -1/8 --- does not satisfy For #c) x = 1/2: 1/2 > 1/8 --- satisfies For #d) x = 2: 2 > 8 --- does not satisfy Thus, x can be in regions #a or #c => x < -1 or 0 < x < 1 Method 2 : x > x^3 => x(x^2 - 1) < 0 => x(x + 1)(x - 1) < 0 Trying x = 2, we have: x(x + 1)(x - 1) = 6 > 0 Thus, we have the curve of x(x + 1)(x - 1) as shown below. Since we needed to solve for x(x + 1)(x - 1) < 0 , the required solutions (regions) which are negative, i.e. below the X-axis, are shown in yellow: 11.JPG Method 3 : x > x^3 => x(x^2 - 1) < 0 => x(x + 1)(x - 1) < 0 We need: 2 of the above 3 terms positive and 1 negative; i.e. x and (x + 1) are positive and (x - 1) is negative => 0 < x < 1 Or All 3 of the above terms negative: i.e. (x -1), x and (x + 1) are negative => x + 1 < 0 => x < -1

Inequality

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards