Basics of Algebra

Algebra Level 2

If

a 2 b + c \frac{a^{2}}{b+c} = b 2 c + a \frac{b^{2}}{c+a} = c 2 a + b \frac{c^{2}}{a+b} = 1 1

Then,find the value of:

1 a + 1 \frac{1}{a+1} + 1 b + 1 \frac{1}{b+1} + 1 c + 1 \frac{1}{c+1}

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The answer is 1.

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Anik Mandal by Anik Mandal , 21, India

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1 solution

Anik Mandal
Sep 7, 2014

1 a + 1 \frac{1}{a+1} + 1 b + 1 \frac{1}{b+1} + 1 c + 1 \frac{1}{c+1}

= a a 2 + a \frac{a}{a^{2}+a} + b b 2 + b \frac{b}{b^{2}+b} + c c 2 + c \frac{c}{c^{2}+c}

= a a + b + c \frac{a}{a+b+c} + b a + b + c \frac{b}{a+b+c} + c a + b + c \frac{c}{a+b+c}

= 1 1

21 Helpful 0 Interesting 0 Brilliant 0 Confused

great yar what a good solution

abdul lah - 6 years, 8 months ago

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