# 9th Class Math Chapter 4 Algebraic Expressions & Algebraic Formulas Short Questions Answer

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## 9th Class Math Chapter 4 Algebraic Expressions & Algebraic Formulas Short Questions Answer

If x + 1/x = 3 find these. x² + 1/x² and x⁴ + 1/x⁴

Solution:

1. (x + 1/x)² = (3)²

x² + 1/x² + 2 = 9

x² + 1/x² = 7

1. (x² + 1/x²)² = (7)²

x⁴ + 1/x⁴ = 47

If x – 1/x = 2 find these. x² + 1/x² and x⁴ + 1/x⁴

Solution:

1. (x – 1/x)² = (2)²

x² + 1/x² – 2 = 4

x² + 1/x² = 4 + 2

x² + 1/x² = 6

1. (x² + 1/x²)² = (6)²

x⁴ + 1/x⁴ + 2 = 36

x⁴ + 1/x⁴ = 36 – 2

x⁴ + 1/x⁴ = 34

Find the value of x³ + y³ and xy of x + y = 5 and x – y = 3

Solution:

x + y = 5, xy = 3

4xy = (x + y)² – (xy

= (5)² – (3)²

xy = 4

Now,

x³ + y³ = (x + y)³ – 3xy(x + y)

= (5)³– 3(4)(5)

= 125 – 60

= 65

If p = 2 + (3)1/2, find:

Solution:

1/p = 1/2+√3 x 2–√3/2–√3

= 2–√3

1. p + 1/p = 2 + √3 + 2 – √3 = 4
2. p – 1/p = 2 + √3 – (2 – √3) = 2√3
3. = p² + 1/p² = (p + 1/p)² – 2 = (4)² – 2 = 16 – 2 = 14
4. = p² – 1/p² = (p + 1/p)(p – 1/p) = 4(2√3) = 8(√3)

Simplify

1/q = 1/√5+2 x √5–2/√5–2 = √5 – 2

1. q + 1/q = √5 + 2 + √5 – 2 = 2√5
2. q – 1/q = √5 + 2 – (√5 – 2) = 4
3. q² + 1/q² = (q + 1/q)² – 2 = (2√5)² – 2 = 20 – 2 = 18
4. q² – 1/q² = (q + 1/q)(q – 1/q) = (2√5)(4) = 8√5

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