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# If (a^2 +b^2)^3=(a^3+b^3)^2 then the numerical value of a/b + b/a is equal to x. Find the value of x.

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If (a^2 +b^2)^3=(a^3+b^3)^2 then the numerical value of a/b + b/a is equal to x. Find the value of x.
May 4, 2015

#2
+27480
+10

heureka beat me to it!

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May 4, 2015

#1
+21356
+10

If then the numerical value of a/b + b/a is equal to x. Find the value of x.

$$\small{\text{ \begin{array}{rcll} (a^2 +b^2)^3 &=& (a^3+b^3)^2 \\ (a^2)^3+3\cdot(a^2)^2\cdot (b^2)^1 +3\cdot (a^2)^1\cdot (b^2)^2 + (b^2)^3 &=& (a^3)^2 + 2\cdot(a^3)^1\cdot (b^3)^1 + (b^3)^2\\ a^6+3\cdot a^4\cdot b^2 +3\cdot a^2\cdot b^4 + b^6 &=& a^6 + 2\cdot a^3\cdot b^3 + b^6\\ \not{a^6}+3\cdot a^4\cdot b^2 +3\cdot a^2\cdot b^4 + \not{b^6} &=& \not{a^6} + 2\cdot a^3\cdot b^3 + \not{b^6}\\ 3\cdot a^4\cdot b^2 +3\cdot a^2\cdot b^4 &=& 2\cdot a^3\cdot b^3 \\ 3\cdot a^4\cdot b^2 +3\cdot a^2\cdot b^4 &=& 2\cdot a^3\cdot b^3 & | \quad : (a^3\cdot b^3) \\ 3\cdot\frac{ a }{ b }+3\cdot \frac{ b } { a } &=& 2 \\ 3\cdot\frac{ a }{ b }+3\cdot \frac{ b } { a } &=& 2 & | \quad : 3 \\ \frac{ a }{ b }+ \frac{ b } { a } &=& \frac{2}{3} \end{array} }}\\ \mathbf{x=\dfrac{ a }{ b }+ \dfrac{ b } { a } &=& \dfrac{2}{3} }$$

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May 4, 2015
#2
+27480
+10

heureka beat me to it!

.

Alan May 4, 2015