Question

If x^2+1/x^2=6 find x^3+1/x^3​

Answer 1

Step-by-step explanation:

x²+1/x²=6

(x+1/x)²-2(x)(1/x)=6

(x+1/x)²-2=6

(x+1/x)²=8

x+1/x=2√2

x³+1/x³=(x+1/x)(x²+1/x²-(x)(1/x))

=(2√2)(6-1)

=2√2(5)

=10√2

x³+1/x³=10√2

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Answer 2

Answer:

What is the value of x^3 +1/x^3,if the value of x^2 +1/x^2 is 6?

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We know, a2+b2=(a+ b)2−2ab. Here, substitute a=x,b=1x. We have,

x2+1x2=(x+1x)2−2(x)(1x)

=> x2+1x2=(x+1x)2−2

Given, x2+1x2=6

=> (x+1x)2=8

=> (x+1x)=±22–√

Now, we want x3+1x3. It can be factorised into:

x3+1x3= (x+1x)(x2+1x2−1)

=> x3+1x3=±22–√∗(6−1)

=> x3+1x3=±102–√

If it is mentioned that x is a positive number, then the value would be 102–√.

Hope this helps!