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Question Number 15561 by Mr easymsn last updated on 11/Jun/17

Commented by Mr easymsn last updated on 11/Jun/17

$$plziknowtheansis2and3butijust$$$$needurworkings$$$$$$

Commented by RasheedSoomro last updated on 11/Jun/17

$$\mathrm{Both}\mathrm{equations}\mathrm{are}\mathrm{symmetric}$$$$\mathrm{that}\mathrm{means}\mathrm{if}(\mathrm{a},\mathrm{b})\mathrm{satisfies}\mathrm{the}$$$$\mathrm{equations}(\mathrm{b},\mathrm{a})\mathrm{also}\mathrm{does}$$$$\mathrm{In}\mathrm{case}\mathrm{x},\mathrm{y}\in \mathbb{N}$$$$\mathrm{possible}\mathrm{values}\mathrm{for}\mathrm{x}\mathrm{are}1,2,3,4$$$$\mathrm{first}\mathrm{equation}\mathrm{suggests}\mathrm{that}\mathrm{respective}$$$$\mathrm{values}\mathrm{of}\mathrm{y}\mathrm{may}\mathrm{be}4,3,2,1$$$$\mathrm{So}\mathrm{trying}\mathrm{these}\mathrm{values}\mathrm{in}\mathrm{second}\mathrm{equation}$$$$1^4+4^1\ne 17$$$$2^3+3^2=8+9=17$$$$\mathrm{Hence}(2,3)\mathrm{\&}(3,2)\mathrm{are}\mathrm{two}\mathrm{solutions}\mathrm{in}\mathbb{N}.$$

Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 12/Jun/17

$$oneofxory,isoddandanotheriseven.$$$$becausesumof2oddnumberor2$$$$evennumberwillbeevenandcannot$$$$beequailto5.\left(oddnumber\right)$$$$so:x=2n,y=2m+1\Rightarrow 2(n+m)+1=5\Rightarrow$$$$m+n=2\Rightarrow m=n=1$$$$\Rightarrow x=2,y=3orx=3,y=2.$$

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