An algebra problem by Jerson Suplemento

Algebra Level 1

a + b = 13 a+b = 13

a b = 40 ab = 40

What is the sum of the squares of a a and b b ?


The answer is 89.

Jerson Suplemento by Jerson Suplemento , 22, Philippines

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3 solutions

a 2 + b 2 = ( a + b ) 2 − 2 a b = ( 13 ) 2 − 2 ( 40 ) = 169 − 80 = 89 a^2 + b^2 = (a+b)^2 - 2ab = (13)^2 -2(40) = 169 - 80 = \boxed{89} .

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Moderator note:

Simple standard approach

the question looks like a+b = 13ab = 40

Chaitnya Shrivastava - 5 years, 9 months ago

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Lol, yeah. Maybe a brilliant moderator will edit that.

Venkata Karthik Bandaru - 5 years, 9 months ago

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maybe someone would do it

Chaitnya Shrivastava - 5 years, 9 months ago
Lew Sterling Jr
May 21, 2019

a + b = 13 a b = 40 40 = ( 40 ⋅ 1 ) 40 = ( 20 ⋅ 2 ) 40 = ( 10 ⋅ 4 ) 40 = ( 5 ⋅ 8 ) 5 + 8 = 13 ( 5 ) ( 8 ) = 50 ( 5 ) 2 + ( 8 ) 2 = ( 25 ) + ( 64 ) = 89 \begin{matrix} a+b=13 & & ab=40\\ &40=(40\cdot 1)&\\ &40=(20\cdot 2)&\\ &40=(10\cdot 4)&\\ &40=(5\cdot 8)&\\\\ 5+8=13&&(5)(8)=50\\ &(5)^2+(8)^2&\\ &=(25)+(64)&\\ &=89&\\ \end{matrix}

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Avik Saha
Aug 24, 2015

we know (a+b)^2=a^2+2 a b+b^2 =>a^2+b^2=(a+b)^2-2 a b =>a^2+b^2=(13)^2-2*40 SO, a^2+b^2=89

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Use LaTeX for better display

Rama Devi - 5 years, 9 months ago

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