What is\sqrt[3]{x}-\frac{1}{\sqrt[3]{x}}?



Answered question


What is x31x3?

Answer & Explanation

Jaden Petersen

Jaden Petersen

Beginner2022-02-03Added 15 answers

Step 1 x31x3 Take out the LCD:x3 x3×x3x31x3 Make their denominators same (x3×x3)1x3 x3×x3=x×x3=x23=x23 ⇒=x231x3
Amiya Wolf

Amiya Wolf

Beginner2022-02-04Added 11 answers

Step 1 Look at these alternative ways of writing roots x is the same as x12 x3 is the same as x13 x4 is the same as x14 So for any number n xn is the same as x1n Step 2 Just picking a number at random I chose 3 Another way (not normally done) of writing 3 is 31 When you have 3×3 it can be written as 32 In the same way 3×3×3 can be written as 33 In the same way 3×3×3×3 can be written as 34 Notice that 3×3=31×31=31+1=32 Notice that 3×3×3=31×31×31=3(1+1+1)=33 Step 3 Given that a way of writing square root of 3 is 3 is 312 Compare what happens in each of the following two rows 31×31×31=31+1+1=33 312×312×312=312+12+12=332 Step 4 You asked about x3x3=x23 From above we know that x3 is the same as x13 But we have x3x3 This is the same as x13×x13=x13+13=x23 Step 5 Backtrack for a moment and again think about x13×x13 Like in 3×3=32 x13×x13=(x13)2 and x13×x13=x13+13=x23 Then (x13)2=x1×23=x23 Turning this back the other way x23=x23 Practise and a lot of it will fix this in your mind.

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