+0  
 
0
56
2
avatar

The real number x and y satisfy

x + y = 4

x^2 + y^2 = 22

x^4 = y^4 - 176√7

 Mar 24, 2020
 #1
avatar+111330 
+1

x + y  = 4

x^2  + y^2   =22

x^4 = y^4  - 176√7

 

Rearranging the last equation we have  that

 

x^4 - y^4  =  -176√7        factor

 

(x^2  - y^2) ( x^2 + y^2)  = -176√7

 

(x + y) ( x - y) ( x^2 + y^2)  = -176√7       subbinng into this we have  that

 

(4) (x - y) ( 22) = -176√7

 

88 ( x - y)  = -176√7         divide both sides by  88

 

x - y =  -2√7

 

So

 

x + y =  4

x - y  =  -2√7      add these

 

2x =  4 - 2√7       divide both sides by 2

 

x =  2 - √7

 

And

 

( 2 - √7)  +  y  = 4

 

y =  4 - (2 - √7)

 

y =  2 + √7

 

 

 

cool cool cool

 Mar 24, 2020
 #2
avatar+1970 
+2

Nice, Chris!

CalTheGreat  Mar 24, 2020

8 Online Users

avatar