Question

Problem

Answer 1

The value of x is ±0.7071 and x is an irrational number

How to solve for x?

The equation is given as:

$4x^2 = 2$

Divide by 4

$x^2 = 0.5$

Take the square roots

$x = \pm 0.7071$

Hence, the value of x is ±0.7071

How to prove that x is irrational?

The equation is given as:

$4^x = 5$

Take the logarithm of both sides

$x\log(4) = \log(5)$

Divide both sides by log(4)

x = 1.16096....

The above number is a non-terminating decimal.

Non-terminating decimals cannot be represented as fractions of two integers

Hence, x is an irrational number

Read more about irrational numbers at:

brainly.com/question/17450097

#SPJ1