If x + 1/x = 5, find the value of x^2 + 1/x^2.

23. Square both sides: (x + 1/x )^2 = x^2 + 2 (x ) (1/x ) + 1/x^2 = x^2 + 2 + 1/x^2 = 25. Subtract the middle term: x^2 + 1/x^2 = 25 - 2 = 23.

If $x + \frac{1}{x} = 5$ , find the value of $x^{2} + \frac{1}{x ^{2}}$ .

Class 9PolynomialsPolynomials

Square both sides:

(x + \frac{1}{x})^{2} = x^{2} + 2 (x) (\frac{1}{x}) + \frac{1}{x ^{2}} = x^{2} + 2 + \frac{1}{x ^{2}} = 25

. Subtract the middle term:

x^{2} + \frac{1}{x ^{2}} = 25 - 2 = 23

Answer: D) 23

By number of terms:
- **Monomial**: 1 term (e.g.

5 x^{3}

)
- **Binomial**: 2 terms (e.g.

x^{2} + 3

)
- **Trinomial**: 3 terms (e.g.

x^{2} + 2 x + 1

)

By degree:
- **Linear** (degree 1):

3 x - 5

- **Quadratic** (degree 2):

x^{2} - 4

- **Cubic** (degree 3):

2 x^{3} + x - 1

- **Biquadratic** (degree 4):

x^{4} + 1

A polynomial can fit multiple categories.

5 x^{3}

is both a monomial and a cubic.

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