It is easy, to get wrong answer!

Algebra Level 5

x 2 + 70 x + 144 = 0 x^2+70x+144=0

Suppose a a and b b are two roots of the above equation. Find the value of ( a + b ) 2 (\sqrt{a}+\sqrt{b})^2 .

-70 -94 -54 -56 -66 -74 -84 -46

Chan Lye Lee by Chan Lye Lee , 44, Singapore

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2 solutions

Chan Lye Lee
Apr 21, 2016

Note that if a a and b b are negative, then a b ≠ a b \sqrt{a}\sqrt{b} \neq \sqrt{ab} . Let a = − m a=-m and b = − n b=-n where m m and n n are positive. Now a b = m n ab=mn and hence a b = − m − n = ( i m ) ( i n ) = − m n = a b \sqrt{a}\sqrt{b} = \sqrt{-m}\sqrt{-n}=(i\sqrt{m})(i\sqrt{n})= -\sqrt{mn}=\sqrt{ab} .

By Vieta's formula, we have a + b = − 70 a+b=-70 and a b = 144 ab=144 . In this case, a a and b b are negative.

Now ( a + b ) 2 = ( a ) 2 + 2 a b + ( b ) 2 = a + b − 2 a b = − 70 − 2 ( 12 ) = − 94 (\sqrt{a}+\sqrt{b})^2 = (\sqrt{a})^2 + 2\sqrt{a}\sqrt{b}+(\sqrt{b})^2 =a+b - 2\sqrt{ab}=-70-2(12)=-94 .

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Om telolet ommmmm @Chan Lye Lee

I Gede Arya Raditya Parameswara - 4 years, 5 months ago
Mohammad Farhat
Jun 11, 2019

Wolfram Alpha is the key!

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