If M = 3 x 2 </msup> &#x2212;<!-- − --> 8 x y + 9 y 2 <

Lydia Carey

Lydia Carey

Answered question

2022-06-07

If M = 3 x 2 8 x y + 9 y 2 4 x + 6 y + 13, where x , y R , then M must be:
a) positive
b) negative
c) 0
d) an integer

Answer & Explanation

Eleanor Luna

Eleanor Luna

Beginner2022-06-08Added 19 answers

Without completing the square, you can also apply the following technique:
3 x 2 4 x ( 2 y + 1 ) + ( 9 y 2 + 6 y + 13 M ) = 0 Δ x = 4 ( 2 y + 1 ) 2 3 ( 9 y 2 + 6 y + 13 M ) 0 3 M 11 y 2 + 2 y + 35 3 M 11 ( y + 1 11 ) 2 + 384 11 3 M 384 11 M 128 11 > 0.

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