Question

x+1/x = 7 , x^2+1/x^3 = 169, x^3+1/x^2 = ?​

Answer 1

Answer:

x3+1/x2 = 200

Step-by-step explanation:

Given

x+1/x = 7

x2+1/x3 = 169

x3+1/x2 = ?

We know that x+1/x = 7

So (x+1/x)2 = 49

x2 + 1/x2 + 2(x)(1/x) = 49

It is known that (x)(1/x) = 1

Therefore x2 + 1/x2 + 2 = 49

                           x2 + 1/x2 = 47 ----------(1)

Once again from x+1/x = 7

We can say that (x+1/x)3 = 343

x3 + 1/x3 + 3(x)(1/x)(x+1/x) = 343

We know that (x)(1/x) = 1 and x+1/x = 7

So x3 + 1/x3 + 3*7 = 343

    x3 + 1/x3 + 21 = 343

    x3 + 1/x3 = 322 ----------(2)

The question asked is x3+1/x2  so we must add (1) and (2).

(1) + (2) => x2 + 1/x2 + x3 + 1/x3 = 322 + 47

We can rewrite this as x2+1/x3 + x3+1/x2 = 369

We know that x2+1/x3 = 169

So we can once again write the equation as

169 + x3+1/x2 = 369

x3+1/x2 = 369 – 169

x3+1/x2 = 200

I hope this is the correct answer. But if the answer is incorrect, this would still be the correct procedure.