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Omni-MATH / Let a,b,c,x be reals with (a+b)(b+c)(c+a)≠0 that satisfy (a²)/(a+b)=(a²)/(a+c)+20, (b²)/(b+c)=(b²)/(b+a)+14, and (c²)/(c+a)=(c²)/(c+b)+x Compute x.

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problem

Let a,b,c,xa, b, c, x be reals with (a+b)(b+c)(c+a)≠0(a+b)(b+c)(c+a) \neq 0 that satisfy a2a+b=a2a+c+20,b2b+c=b2b+a+14, and c2c+a=c2c+b+x\frac{a^{2}}{a+b}=\frac{a^{2}}{a+c}+20, \quad \frac{b^{2}}{b+c}=\frac{b^{2}}{b+a}+14, \quad \text { and } \quad \frac{c^{2}}{c+a}=\frac{c^{2}}{c+b}+x Compute xx.
Plain-text mathematical notation (without MathML)
Let a,b,c,x be reals with (a+b)(b+c)(c+a)≠0 that satisfy (a²)/(a+b)=(a²)/(a+c)+20, (b²)/(b+c)=(b²)/(b+a)+14,  and  (c²)/(c+a)=(c²)/(c+b)+x Compute x.
Original LaTeX notation
Let $a, b, c, x$ be reals with $(a+b)(b+c)(c+a) \neq 0$ that satisfy $$\frac{a^{2}}{a+b}=\frac{a^{2}}{a+c}+20, \quad \frac{b^{2}}{b+c}=\frac{b^{2}}{b+a}+14, \quad \text { and } \quad \frac{c^{2}}{c+a}=\frac{c^{2}}{c+b}+x$$ Compute $x$.

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Source and history

task_id
84e422e9-0bcf-5128-955e-cf85dfc04107
task_key
test--84e422e9-0bcf-5128-955e-cf85dfc04107
task_revision_id
1
config / split
/ test

Official source

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