Question

maths polynomials....​

Answer 1

Answer:

Option (B)

Step-by-step explanation:

Given :-

x+(1/x) = 5

To find :-

The value of (x⁴+1)/x²

Solution :-

Given that

x+(1/x) = 5

On squaring both sides then

=> [x+(1/x)]² = 5²

=> x²+2(x)(1/x)+(1/x)² = 5×5

Since, (a+b)² = a²+2ab+b²

Where, a = x and b = 1/x

=> x²+2(x/x) +(1/x²) = 25

=> x²+2(1) +(1/x²) = 25

=> x²+2+(1/x²) = 25

=> x²+(1/x²) +2 = 25

=> x²+(1/x²) = 25-2

=> x²+(1/x²) = 23

=> [(x²×x²)+1]/x² = 23

=> (x⁴+1)/x² = 23

Answer :-

The value of (x⁴+1)/x² is 23

Used formulae:-

→ (a+b)² = a²+2ab+b²

Answer 2

$\implies x + \frac{1}{x} = 5 - - (1)\\ \\ \\ \implies \: \frac{x {}^{4} + 1}{x {}^{2} } \\ \\ \implies \: \frac{x {}^{ \cancel{4}} }{x {}^{ \cancel{2}} } + \frac{1}{x {}^{2} } \\ \\ \\ \implies \: {x}^{2} + \frac{1}{ {x}^{2} } - - - (2) \\ \\ \eq \: 1 \: square \: both \: side \\ \\ \\ \implies \: {x}^{2} + ( \frac{1}{x}) {}^{2} + 2. \cancel{x. \frac{1}{1}} = {5}^{2} \\ \\ \\ \implies \: {x}^{2} + \frac{1}{x {}^{2} } =25 - 2 \\ \\ \\ \implies \: {x}^{2} + \frac{1}{ {x}^{2} } = 23$

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option b is correct✅✔

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thanks