If x + y + z = 9 and xy + yz + zx = 23, find x² + y² + z².

35. (x + y + z)² = x² + y² + z² + 2(xy + yz + zx). So 9² = x² + y² + z² + 2(23), i.e. 81 = x² + y² + z² + 46, giving x² + y² + z² = 35. Remember to DOUBLE the 23.

If $x + y + z = 9$ and $x y + yz + z x = 23$ , find $x^{2} + y^{2} + z^{2}$ .

Class 9PolynomialsPolynomials

A58
B127
C104
D35

Step-by-Step Solution

(x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2 (x y + yz + z x)

. So

9^{2} = x^{2} + y^{2} + z^{2} + 2 (23)

, i.e.

81 = x^{2} + y^{2} + z^{2} + 46

, giving

x^{2} + y^{2} + z^{2} = 35

. Remember to DOUBLE the 23.

Answer: D) 35

Key idea: Naming polynomials by terms and degree

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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If x+y+z=9 and xy+yz+zx=23, find x2+y2+z2.

Step-by-Step Solution

Key idea: Naming polynomials by terms and degree

Master this chapter in 30 minutes a day.

More Class 9 Polynomials practice

If $x + y + z = 9$ and $x y + yz + z x = 23$ , find $x^{2} + y^{2} + z^{2}$ .