What's a?!
a x − 2 2 4 x 2 + 2 5 x − 4 7 = − 8 x − 3 − a x − 2 5 3
The equation above, where a is a constant, holds true for all values of x = a 2 . What is the value of a ?
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2 solutions
Same explanation, so I'm not going to write it. Great work!
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Thanks, can you upvote?
Very well, I am impressed!
ANSWER EXPLANATION: There are two ways to solve this question. The faster way is to multiply each side of the given equation by a x − 2 (so you can get rid of the fraction). When you multiply each side by a x − 2 , you should have:
2 4 x 2 + 2 5 x − 4 7 = ( − 8 x − 3 ) ( a x − 2 ) − 5 3
You should then multiply ( − 8 x − 3 ) and (ax−2) using FOIL.
2 4 x 2 + 2 5 x − 4 7 = − 8 a x 2 − 3 a x + 1 6 x + 6 − 5 3
Then, reduce on the right side of the equation
2 4 x 2 + 2 5 x − 4 7 = − 8 a x 2 − 3 a x + 1 6 x − 4 7
Since the coefficients of the x 2 -term have to be equal on both sides of the equation, − 8 a = 2 4 , or a = − 3 .
The final answer is B.
a x − 2 2 4 x 2 + 2 5 x − 4 7 = − 8 x − 3 − a x − 2 5 3 = a x − 2 − 8 a x 2 + ( 1 6 − 3 a ) x + 6 − 5 3
Equating the coefficient of x 2 on both sides, we have − 8 a = 2 4 ⟹ a = − 3 . Note that 1 6 − 3 a = 2 5 . Therefore, a = − 3 .