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Let u and v be the solutions to 3x^2 + 5x + 7 = -4x^2 + 3x - 14.  Find 1/u^2 + 1/v^2.

 Mar 19, 2024
 #1
avatar+128794 
+1

Simplify as

7x^2 + 2x + 21  =  0 

uv =  21 / 7   = 3

(uv)^2   = 9

u + v = -2/7      square both sides

u^2 + 2uv + v^2  = 4/49

u^2  + v^2  + 2(3)  =4/49

u^2 + v^2  =  4/49 - 6

u^2 + v^2 =  -290 /  49

 

1/u^2  + 1/v^2   =  [ u^2 + v^2 ] / (uv)^2  =  [ -290 / 49 ]  / [ 9 ]   =  -290 / 441

 

cool cool cool

 Mar 19, 2024

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