Mathematics: If = 1 and a 0, find the value of

If = 1 and a 0, find the value of - id103359133, kevinvalencia01

TeenOlaflover

07.01.2022

Some factoring lets us write

$a^{2b}-\dfrac1{a^b}=a^{2b}-a^{-b}=a^{-b}(a^{3b}-1)$

Then

$8a^{3b}=1\implies a^{3b}=\dfrac18$

$a^{2b}-\dfrac1{a^b}=a^{-b}\left(\dfrac18-1\right)=-\dfrac78a^{-b}=-\dfrac7{8a^b}$

Taking the cube root to solve for , we find

$\sqrt[3]{a^{3b}}=\sqrt[3]{\dfrac18}\implies a^b=\dfrac12$

so ultimately

$a^{2b}-\dfrac1{a^b}=-\dfrac7{8\cdot\frac12}=-\dfrac74$

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Benitez0212

07.01.2022

The value of the given expression is 1 - 1 = 0

Step-by-step explanation:

8a^{3b} = 1 can be rewritten as (8a³)^b = 1 = (8a³)^0, which indicates that b = 0. If b= 0, then 2b = 2(0) = 0.

Then a^(2b) = a^0 = 1, and 1/a^b = 1/1 = 1.

Thus, the value of the given expression is 1 - 1 = 0

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jazzy1926

08.11.2022

a = sqrt(2)

Step-by-step explanation:

This is a right triangle so we can use trig functions

sin theta = opp / hyp

sin 30 = a / 2 sqrt(2)

2 sqrt(2) sin 30= a

2 sqrt(2) * 1/2 =a

sqrt(2) =a

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