+0  
 
0
530
2
avatar
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.
Guest May 4, 2015

Best Answer 

 #2
avatar+26328 
+10

 a/b + b/a

 

heureka beat me to it!

.

Alan  May 4, 2015
Sort: 

2+0 Answers

 #1
avatar+18712 
+10

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

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

heureka  May 4, 2015
 #2
avatar+26328 
+10
Best Answer

 a/b + b/a

 

heureka beat me to it!

.

Alan  May 4, 2015

13 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details