Hor Kuok Theng's answer to Chelsea's Secondary 4 E Maths Singapore question.
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X² - 8X + (a² - 5)² is a perfect square, meaning that it can be written in the form of ( X - (a² - 5) )² or ( (a² - 5) - X )²
As such, there are two possible values of a.
We know frow that the expansion of (a - b)² results in a² - 2ab + b² , and the -8 in the question is the "-2ab"
So -2 (a²-5) X is equal to -8X and (a²-5) = 4 or -4
There are two values of a that satisfy this,
a = 1 and a = 3
when a = 1, (a²-5) = -4.
when a = 3, (a²-5) = 4
As such, there are two possible values of a.
We know frow that the expansion of (a - b)² results in a² - 2ab + b² , and the -8 in the question is the "-2ab"
So -2 (a²-5) X is equal to -8X and (a²-5) = 4 or -4
There are two values of a that satisfy this,
a = 1 and a = 3
when a = 1, (a²-5) = -4.
when a = 3, (a²-5) = 4
Date Posted:
4 years ago
Actually four values -3, -1, 1 and 3, and there is the given condition that a > 1 from the question.
Hence, a = 3.
Hence, a = 3.
Yep! Still have to reject the value of a = 1.
Didn't bother considering a of negative values as we can see that a won't be negative from the conditions.
Didn't bother considering a of negative values as we can see that a won't be negative from the conditions.
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