Question

If x = √5 + √3 , then the value of x^4 - 16x^2 +5 = ?​

Answer 1

Answer:

The value of x^4 - 16x^2 +5 =1.

✔️Hope it will help you.✔️

Answer 2

Given that x = √5 + √3

so, x² = x.x

therefore x² = (√5 + √3)²

x² = 5 + 2√15 + 3

x² = 8 + 2√15

and for x⁴,

x⁴ = x².x²

x⁴ = (8 + 2√15)²

x⁴ = 64 + 60 + 32√15 = 124 + 32√15

Now it is asked that,

x⁴ - 16x² + 5 =?

so,

125 + 32√15 - 16(8 + 2√15) + 5

=125 + 32√15 - 128 - 32√15 + 5

=2.

2 is the final answer.

I hope this may help you.

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