Question 935127: If a^2-mab+1/4b^2 is a perfect square, then what is the value of m? And why? Thanks! Found 3 solutions by algebrahouse.com, TimothyLamb, MathTherapy:Answer by algebrahouse.com(1659) (Show Source):
You can put this solution on YOUR website! A perfect square trinomial could be in the form:
a² - 2ab + b² factoring into (a - b)², which is (a - b)(a - b)
or
a² + 2ab + b² factoring into (a + b)², which is (a + b)(a + b)
If a² - mab + (1/4)b² is a perfect square trinomial,
it would factor into (a - 1/2)(a - 1/2) {the square root of a² is a, and the square root of 1/4 is 1/2}
If you multiply (a - 1/2)(a - 1/2)
= a² - (1/2)ab - (1/2)ab - (1/2)(-1/2) {used foil method}
= a² - ab + 1/4 {combined like terms and multiplied}
You can put this solution on YOUR website! a perfect square in a and b:
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( a - (1/2)b )( a - (1/2)b )
aa - (1/2)ab - (1/2)ab + (1/4)bb
aa - (1/4)ab + (1/4)bb
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given:
a^2 - mab + (1/4)b^2
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answer:
m = 1/4
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