Quadratic

Algebra Level 3

If ${ x }^{ 2 }+3x-1=0$ , what is the value of ${ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } }$ ?

from MTAP Math Challenge Team Orals

2 solutions

Parveen Soni
Nov 9, 2014

Divide given equation by x we have
x+3-1/x=0 i.e x-1/x=-3 now squaring both sides we have
x^2+1/x^2-2=9 hence x^2+1/x^2=11

Did in the same way. :D

satvik pandey - 6 years, 7 months ago

Smarth Mittal
Feb 20, 2015

The given equation is ${x}^2 + 3x - 1 = 0$

Let 'a' and 'b' be the two roots of the equation

So * $a+b$ = -3

* $ab$ = -1

So * a = $\frac{1}{b}$

Hence we get * $a + \frac{1}{a}$ = -3

Squaring both sides we get the solution as 11