Question

PLEASE SOLVE THIS QUESTION
GOOD ANSWER IS BRAINLEIST​

Answer 1

solution

$x = m {}^{4} + m {}^{5} = m{}^{4} (1 + m) \\ and \: y = m {}^{9}$

so it is obvious that..

$m {}^{9} > m {}^{4} (1 + m)$

therefore...

y>x

Answer 2

Question

x = m⁴ + m^5 and y = m^9, where m is a positive integer greater than 1.

Which of these can be said about the relationship between x and y?

A) x > y

B) x < y

C) x = y

D) We can not say without knowing the value of m

$\rule{100}2$

Answer

Option b) x < y

$\rule{100}2$

Explanation

Given,

x = $\sf m^4 + m^5$

and, y = $\sf m^9$

Taking the ratio of x and y,

$\sf\frac{x}{y} = \frac{m^4 + m^5}{m^9}$

$\sf\frac{x}{y} = \frac{m^4(1 + m)}{m^9}$

$\sf\frac{x}{y} = \frac{1+m}{m^5}$

Now, for any positive integer greater than 1,

$\sf\frac{1 + m}{m^5} < 1$

$\sf\implies\frac{x}{y} < 1$

$\sf\implies x < y$