Maths help?

1 Answer

An even integer raised to any positive integral power is even: . $\text{(even)}^n \:=\:\text{even}$

An odd integer raised to any positive integral power is odd: . $\text{(odd)}^n \:=\:\text{odd}$

We have: $\bigg[x^{10} + px^9 + rx^4\bigg] - \bigg[qx^7 + s\bigg] \;=\;0$

Suppose x is even.

We have: $\bigg[(even)^{10} + p(even)^9 + r(even)^4\bigg] - \bigg[q(even)^7 + (odd)\bigg] \;=\;0$ [Since s is odd]

$\underbrace{\bigg[(even) + (even) + (even)\bigg]}_{\text{(even)}} - \underbrace{\bigg[(even) + (odd)\bigg]}_{\text{(odd)}} \;=\;0$

And the difference of an even number and an odd number cannot be zero.

Suppose x is odd.

We have: $\bigg[(odd)^{10} + p(odd)^9 + r(odd)^4\bigg] - \bigg[r(odd)^4 + (odd)\bigg] \;=\;0$

$\underbrace{\bigg[(odd) + (odd) + (odd)\bigg]}_{\text{(odd)}} - \underbrace{\bigg[(odd) + (odd)\bigg]}_{\text{(even)}} \;=\;0$

And the difference of an odd number and an even number cannot be zero.