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Question Number 8946 by ridwan balatif last updated on 07/Nov/16

x−y=1 and x^y =64, what is the value of x+y=...?

$$\mathrm{x}−\mathrm{y}=\mathrm{1}\:\mathrm{and}\:\mathrm{x}^{\mathrm{y}} =\mathrm{64},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}=...? \\ $$

Answered by Rasheed Soomro last updated on 07/Nov/16

x−y=1 and x^y =64, what is the value of x+y=...? y=x−1, x^(x−1) =64⇒x is comprising of only factor 2. I-e x=2,4,8,... If x=2, x^(x−1) =2^(2−1) =2≠64,So x≠2 If x=4, x^(x−1) =4^(4−1) =4^3 =64,So x=4 x=4⇒y=x−1=4−1=3 Hence x+y=4+3=7

$$\mathrm{x}−\mathrm{y}=\mathrm{1}\:\mathrm{and}\:\mathrm{x}^{\mathrm{y}} =\mathrm{64},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}=...? \\ $$$$\mathrm{y}=\mathrm{x}−\mathrm{1},\:\mathrm{x}^{\mathrm{x}−\mathrm{1}} =\mathrm{64}\Rightarrow\mathrm{x}\:\mathrm{is}\:\mathrm{comprising}\:\mathrm{of}\:\mathrm{only}\:\mathrm{factor}\:\mathrm{2}. \\ $$$$\mathrm{I}-\mathrm{e}\:\:\mathrm{x}=\mathrm{2},\mathrm{4},\mathrm{8},... \\ $$$$\mathrm{If}\:\mathrm{x}=\mathrm{2},\:\mathrm{x}^{\mathrm{x}−\mathrm{1}} =\mathrm{2}^{\mathrm{2}−\mathrm{1}} =\mathrm{2}\neq\mathrm{64},\mathrm{So}\:\mathrm{x}\neq\mathrm{2} \\ $$$$\mathrm{If}\:\mathrm{x}=\mathrm{4},\:\mathrm{x}^{\mathrm{x}−\mathrm{1}} =\mathrm{4}^{\mathrm{4}−\mathrm{1}} =\mathrm{4}^{\mathrm{3}} =\mathrm{64},\mathrm{So}\:\mathrm{x}=\mathrm{4} \\ $$$$\mathrm{x}=\mathrm{4}\Rightarrow\mathrm{y}=\mathrm{x}−\mathrm{1}=\mathrm{4}−\mathrm{1}=\mathrm{3} \\ $$$$\mathrm{Hence}\:\mathrm{x}+\mathrm{y}=\mathrm{4}+\mathrm{3}=\mathrm{7} \\ $$

Commented by ridwan balatif last updated on 07/Nov/16

excuse me, i think x=4 not x=3

$$\mathrm{excuse}\:\mathrm{me},\:\mathrm{i}\:\mathrm{think}\:\mathrm{x}=\mathrm{4}\:\mathrm{not}\:\mathrm{x}=\mathrm{3} \\ $$

Commented by ridwan balatif last updated on 07/Nov/16

thank you sir

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

Commented by Rasheed Soomro last updated on 07/Nov/16

Sorry for mistake. I have corrected now!

$$\mathrm{Sorry}\:\mathrm{for}\:\mathrm{mistake}.\:\mathrm{I}\:\mathrm{have}\:\mathrm{corrected}\:\mathrm{now}! \\ $$

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