Question

if x^2+1/9x^2=25/36 find x^3+1/27x^3

Answer 1

x3+127x3=±91216

Explanation:

Here's an alternative method that does not require calculating x:

Note that:

(x+13x)2=x2+23+19x2=2536+23=4936=(76)2

So:

(x+13x)=±76

Then:

±343216=(x+13x)3

±343216=x3+x+13x+127x3

±343216=x3+127x3±76

So:

x3+127x3=±(343216−76)=±(343216−252216)=±91216