An algebra problem by ANKUSH BHOWMIK

Algebra Level pending

( x + 1 ) 2 + ( x + 3 ) 2 + ( x − 9 ) 2 = 0 \large (x+1)^{2}+(x+3)^{2}+(x-9)^{2}=0

Find all the real roots of the equation above.

There are no real roots x = 9 , − 3 , − 1 x=9,-3,-1 x = 0 x=0 x = 2 , 3 , 9 x=2,3,9

Ankush Bhowmik by ANKUSH BHOWMIK , 19, India

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.

1 solution

Chew-Seong Cheong
Apr 15, 2017

Since ( x + 1 ) 2 (x+1)^2 , ( x + 3 ) 2 (x+3)^2 and ( x − 9 ) 2 (x-9)^2 cannot be simultaneously equal to zero, ( x + 1 ) 2 + ( x + 3 ) 2 + ( x − 9 ) 2 > 0 (x+1)^2+(x+3)^2+(x-9)^2 > 0 for all x x . Therefore, there is no root .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Wrong. The roots are 5 ± 2 i 62 3 \dfrac{5 \pm 2i \sqrt{62}}3 .

Pi Han Goh - 4 years, 1 month ago

I agree with Pi-han, there are no 'real' roots

Aditya Narayan Sharma - 4 years, 1 month ago

Log in to reply

Thanks. I've updated the problem statement to reflect this.

In future, if you notice such errors, you can report the problem directly by selecting that option in the menu.

Brilliant Mathematics Staff - 4 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...