The value of x is ±0.7071 and x is an irrational number
How to solve for x?
The equation is given as:
[tex]4x^2 = 2[/tex]
Divide by 4
[tex]x^2 = 0.5[/tex]
Take the square roots
[tex]x = \pm 0.7071[/tex]
Hence, the value of x is ±0.7071
How to prove that x is irrational?
The equation is given as:
[tex]4^x = 5[/tex]
Take the logarithm of both sides
[tex]x\log(4) = \log(5)[/tex]
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:
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