Question

x^y+y^x=718. what's the value of x-y
${x}^{y} + {y}^{x } = 718$
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Answer 1

Answer:

The value of x - y is 716

Step-by-step explanation:

Given:

$\bf\,x^y+y^x=718$

Take x=717 and y=1

Then,

$x^y+y^x$

$=717^1+1^{717}$

$=717+1$

$=718$

Now,

$x-y=717-1=716$

Answer 2

The value of x - y is 716 or -716

Step-by-step explanation:

Given: $x^y+y^x=718$

To find: x-y

Using hit and trial error method.

• Put y=0 and solve for x

$\Rightarrow x^0+0^x$

$\Rightarrow 1+0$

$\Rightarrow 1\neq 718$  No solution

• Put y=1 and solve for x

$\Rightarrow x^1+1^x$

$\Rightarrow x+1$

$\Rightarrow x+1= 718$

$\Rightarrow x=717$

Possible solution: (717,1)

Therefore,  x - y

x - y = 717 - 1 = 716

We can switch x and y, possible solution (1,717)

x - y = 1 - 717 = -716  

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