Ugly Square Roots

Algebra Level 5

( x 2 + 2 x − 63 ) ( x 2 − 2 x − 63 ) + ( x 2 + 8 x − 33 ) ( x 2 − 8 x − 33 ) = 96 ∣ x ∣ x \sqrt{(x^2+2x-63)(x^2-2x-63)}+\sqrt{(x^2+8x-33)(x^2-8x-33)}=\frac{96|x|}x

Find x 2 x^2


The answer is 130.

View wiki
X X by X X , 17, Taiwan

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Suhas Sheikh
May 30, 2018

Just convert it as x^2-a^2 and x^2-b^2 And then set x^2=t Everything else is easy computation

2 Helpful 0 Interesting 0 Brilliant 0 Confused

@Saitama Lawliet Well, that is what I did too...but, just wondering is there any quicker method?? Coz those easy computations also take some time......!!

Aaghaz Mahajan - 3 years ago
C Anshul
Jul 17, 2018

H i n t s : Hints:

( x 2 − 63 ) 2 − 4 x 2 + ( x 2 − 33 ) 2 − 64 x 2 = 96 \sqrt{(x^{2}-63)^{2}-4x^{2}} + \sqrt{(x^{2}-33)^{2}-64x^{2}} =96

x 4 − 130 x 2 + 6 3 2 + x 4 − 130 x 2 + 3 3 2 = 96 \sqrt{x^{4}-130x^{2}+63^{2}}+\sqrt{x^{4}-130x^{2}+33^{2}}=96

Put t = x 4 − 130 x 2 t=x^{4}-130x^{2}

t + 6 3 2 + t + 3 3 2 = 96 \sqrt{t+63^{2}}+\sqrt{t+33^{2}}=96

Then i just saw 63 + 33 = 96 63+33=96 .

hence t = 0 t=0

x 2 = 130 x^{2}=130

x x cant be zero . Not in domain

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...