Basic Algebra

Algebra Level 2

Positive real numbers x x , y y satisfy the equations x 2 + y 2 = 1 x^2 + y^2 = 1 and x 4 + y 4 = 17 18 x^4 + y^4 = \dfrac {17}{18} . If the positive value of x y xy be expressed as a b \dfrac{a}{b} , for coprime a a and b b , then find the value of a + b a+b .


The answer is 7.

Danish Ahmed by Danish Ahmed , 24, 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

Danish Ahmed
Nov 27, 2015

( x 2 + y 2 ) 2 = x 4 + 2 ∗ ( x y ) 2 + y 4 = 1 (x^2+y^2)^2=x^4+2*(xy)^2+y^4=1

2 ∗ ( x y ) 2 = 1 18 2*(xy)^2=\dfrac{1}{18}

x y = 1 36 xy=\sqrt{\dfrac{1}{36}}

x y = 1 6 xy=\dfrac{1}{6}

2 Helpful 0 Interesting 2 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...