Straightforward?

Algebra Level 1

Let a , b a,b are integers such that:

b ( b + 18 ) = ( a − 9 ) ( a + 9 ) b(b+18)=(a-9)(a+9)

Find a b + 9 \frac{a}{b+9}

If there is insufficient information, give the answer as 0 0


The answer is 0.

Nanayaranaraknas Vahdam by Nanayaranaraknas Vahdam , 22, India

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3 solutions

b ( b + 18 ) = ( a − 9 ) ( a + 9 ) ⇒ b 2 + 18 b + 81 = a 2 ⇒ ( b + 9 ) 2 = a 2 ⇒ a = ± ( b + 9 ) b(b+18)=(a-9)(a+9) \Rightarrow b^{2}+18b+81=a^{2} \Rightarrow (b+9)^2=a^2 \Rightarrow a=\pm(b+9) .

Thus, a b + 9 = ± a a \frac{a}{b+9}=\pm\frac{a}{a} . However, the fraction is equal to ± 1 \pm1 , iff a ≠ 0 a\neq0 , which is not specified. Thus, there is not enough information.

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Same solution.

Sharky Kesa - 7 years ago

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And me.. :D

Karen Vardanyan - 7 years ago

Haha, me too.

Finn Hulse - 7 years ago

there are two variables and just one equation. according to algebra, there should be one equation per unknown term.

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Ryan Redz
Jun 21, 2014

the answer can be +-1

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