Question

Please tell these answers step by step , Refer to the attachment​

Answer 1

Answer:

May it be helpful for you dear.I am less confused by question no. 4...so sry.

Answer 2

Question 1) :-

a) (3x - 1/2x)²

using (a - b)² = a² + b² - 2ab

→ (3x)² + (1/2x)² - 2 * 3x * 1/2x

→ [9x² + (1/4x²) - 3] (Ans.)

b) (2x - 1/3y)³

using (a - b)³ = a³ - b³ - 3ab(a - b)

→ (2x)³ - (1/3y)³ - 3 * 2x * 1/3y (2x - 1/3y)

→ 8x³ - 1/27y³ - (2x/y)(2x - 1/3y)

→ [8x³ - (1/27y³) - (4x²/y) + (2x/3y²)] (Ans.)

c) (1/2x - 2/3y - 4/5z)²

using (a - b - c)² = a² + b² + c² - 2ab + 2bc - 2ca ,

→ (x/2)² + (2y/3)² + (4z/5)² - 2 * (x/2) * (2y/3) + 2 * (2y/3) * (4z/5) - 2 * (4z/5) * (x/2)

→ [(x²/4) + (4y²/9) + (16z²/25) - (2xy/3) + (16yz/15) - (4xz/5)] (Ans.)

Question 2) :-

a) (x - 2/x)(x² + 2 + 4/x²)

→ (x - 2/x){(x)² + (x * 2/x) + (2/x)²}

using (a - b)(a² + ab + b²) = a³ - b³,

→ (x³ - 8/x³) (Ans.)

b) (3a - 2b)(9a² + 6ab + 4b²) - (2a + 3b)(4a² - 6ab + 9b²)

→ [(3a - 2b)(9a² + 6ab + 4b²)] - [(2a + 3b)(4a² - 6ab + 9b²)]

• (a - b)(a² + ab + b²) = (a³ - b³)
• (a + b)(a² - ab + b²) = (a³ + b³)

→ [(3a)³ - (2b)³] - [(2a)³ + (3b)³]

→ 27a³ - 8a³ - 8b³ - 27b³

→ (18a³ - 35b³) (Ans.)

Question 3) :-

→ x = (2y + 6)

cubing both sides ,

→ x³ = (2y + 6)³

→ x³ = 8y³ + 216 + 3*2y*6(2y + 6)

→ x³ = 8y³ + 216 + 36xy

→ x³ - 8y³ - 36xy - 216 = 0 (Ans.)

Question 4) :-

→ 1/(a² - bc) + 1/(b² - ca) + 1/(c² - ab)

since ab + bc + ca = 0 , so,

• (-ab) = bc + ca
• (-bc) = ab + ca
• (-ca) = ab + bc

putting these values,

→ 1/(a² + ab + ca) + 1/(b² + ab + bc) + 1/(c² + bc + ca)

→ 1/a(a + b + c) + 1/b(a + b + c) + 1/c(a + b + c)

→ 1/(a + b + c)[ 1/a + 1/b + 1/c ]

→ 1/(a + b + c)[ (ab + bc + ca)/abc ]

putting ab + bc + ca = 0,

→ 1/(a + b + c) (0 / abc)

→ 0 (Ans.)

Question 5) :-

→ (x - 1/x) = 5

squaring both sides

→ x² + 1/x² - 2 * x * 1/x = 25

→ x² + 1/x² = 25 + 2

→ x² + 1/x² = 27 .

now,

→ x² + 1/x² = 27

squaring both sides ,

→ x⁴ + 1/x⁴ + 2 * x² * 1/x² = 729

→ x⁴ + 1/x⁴ = 729 - 2

→ x⁴ + 1/x⁴ = 727 .

Learn more :-

Let a, b and c be non-zero real numbers satisfying (a³)/(b³ + c³) + (b³)/(c³ + a³) + (c³)/(a³ + b³)

https://brainly.in/question/40626097

https://brainly.in/question/20858452

if a²+ab+b²=25

b²+bc+c²=49

c²+ca+a²=64

Then, find the value of

(a+b+c)² - 100 = __

https://brainly.in/question/16231132