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Find the unique pair of real numbers (x,y) satisfying 

(3x^2 + 6x + 5)(2y^2 + 8y + 10) = 4.

 May 12, 2021
 #1
avatar+2193 
+1

(3x^2 + 6x + 5)(2y^2 + 8y + 10) = 4

(3x^2 + 6x + 5)(y^2 + 4y + 5) = 2

So

3x^2 + 6x + 5 = 2

y^2 + 4y + 5 = 1

Solve for x and y. :)

 

=^._.^=

 May 12, 2021
 #2
avatar+34306 
+1

(-1, -2 )     via the quadratic formula (assigning each half of the left side = 2)

 May 12, 2021

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