Find a + b a+b

Algebra Level 2

{ a 2 + b 2 = 41 a b = 4 \large {\begin{cases} a^2+b^2 = 41 \\ ab=4 \end{cases}}

If a a and b b satisfy the system of equations above, find the absolute value of a + b a+b .


The answer is 7.

Sarthak Chittawar by Sarthak Chittawar , 18, India

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2 solutions

⟹ a 2 + b 2 = ( a + b ) 2 − 2 a b \implies a^2+b^2=(a+b)^2-2ab

⟹ ( a + b ) 2 − 2 × 4 = 41 \implies (a+b)^2-2×4=41

⟹ ∣ a + b ∣ = 7 \implies |a+b|=\boxed{7}

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Sarthak Chittawar
Sep 29, 2016

(a+b)^{2}=a^{2} + b^{2} + 2ab =(a+b)^{2}=41 + 2 \times 4 =(a+b)^{2}=41+8 {Using (a+b)^{2}=a^{2} + b^{2} + 2ab =(a+b)^{2}=49 =a+b=\sqrt{49} =\boxed{a+b=7}

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What about -7 ?

Sabhrant Sachan - 4 years, 8 months ago

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That is also correct. But, 7 is absolute value of the answer.

Sarthak Chittawar - 4 years, 8 months ago

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