If.... $\frac{a}{b} + \frac{b}{a} = 10$ $a/b + b/a = 10$ And... $\frac{a^{2}}{b^{2}} + \frac{b^{2}}{a^{2}} = 98$ $a^2/b^2 + b^2/a^2 = 98$ Find... $\frac{a^{3}}{b^{3}} + \frac{b^{3}}{a^{3}}$ $a^3/b^3 + b^3/a^3$ Also can anyone find a formula to generate higher powers??

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If.... $\frac{a}{b} + \frac{b}{a} = 10$ $a/b + b/a = 10$ And... $\frac{a^{2}}{b^{2}} + \frac{b^{2}}{a^{2}} = 98$ $a^2/b^2 + b^2/a^2 = 98$ Find... $\frac{a^{3}}{b^{3}} + \frac{b^{3}}{a^{3}}$ $a^3/b^3 + b^3/a^3$ Also can anyone find a formula to generate higher powers??

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Answer 1 · 2017-11-26T21:08:55

$970$ $970$

Explanation:

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$\frac{a}{b} + \frac{b}{a} = 10$ $a/b+b/a=10$

$\frac{a^{2} + b^{2}}{a b} = 10$ $(a^2+b^2)/(ab)=10$

$a^{2} + b^{2} = 10 a b$ $a^2+b^2=10ab$

$\frac{a^{2}}{b^{2}} + \frac{b^{2}}{a^{2}} = 98$ $a^2/b^2+b^2/a^2=98$

$\frac{a^{4} + b^{4}}{a^{2} b^{2}} = 98$ $(a^4+b^4)/(a^2b^2)=98$

$a^{4} + b^{4} = 98 a^{2} b^{2}$ $a^4+b^4=98a^2b^2$

$\frac{a^{3}}{b^{3}} + \frac{b^{3}}{a^{3}} = \frac{a^{6} + b^{6}}{a^{3} b^{3}} = \frac{(a^{2} + b^{2}) (a^{4} - a^{2} b^{2} + b^{4})}{a^{3} b^{3}} =$ $a^3/b^3+b^3/a^3=(a^6+b^6)/(a^3b^3)=((a^2+b^2)(a^4-a^2b^2+b^4))/(a^3b^3)=$

$\frac{10 a b (98 a^{2} b^{2} - a^{2} b^{2})}{a^{3} b^{3}} = \frac{10 a b (97 a^{2} b^{2})}{a^{3} b^{3}} = \frac{970 a^{3} b^{3}}{a^{3} b^{3}} = 970$ $(10ab(98a^2b^2-a^2b^2))/(a^3b^3)=(10ab(97a^2b^2))/(a^3b^3)=(970a^3b^3)/(a^3b^3)=970$

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If.... $\frac{a}{b} + \frac{b}{a} = 10$ $a/b + b/a = 10$ And... $\frac{a^{2}}{b^{2}} + \frac{b^{2}}{a^{2}} = 98$ $a^2/b^2 + b^2/a^2 = 98$ Find... $\frac{a^{3}}{b^{3}} + \frac{b^{3}}{a^{3}}$ $a^3/b^3 + b^3/a^3$ Also can anyone find a formula to generate higher powers??

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Explanation:

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If.... ab+ba=10a/b + b/a = 10 And... a2b2+b2a2=98a^2/b^2 + b^2/a^2 = 98 Find... a3b3+b3a3a^3/b^3 + b^3/a^3 Also can anyone find a formula to generate higher powers??

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If.... $\frac{a}{b} + \frac{b}{a} = 10$ $a/b + b/a = 10$ And... $\frac{a^{2}}{b^{2}} + \frac{b^{2}}{a^{2}} = 98$ $a^2/b^2 + b^2/a^2 = 98$ Find... $\frac{a^{3}}{b^{3}} + \frac{b^{3}}{a^{3}}$ $a^3/b^3 + b^3/a^3$ Also can anyone find a formula to generate higher powers??