Question

if (3+5/x)(9-15/x+25/x)=3, then find the value of (3-5/x)(9+15/x+25/x^2) and hence find x.​

Answer 1

Correct Question :- if (3+5/x)(9 - 15/x + 25/x²) = 3, then find the value of (3 - 5/x)(9+15/x+25/x²) and hence find x. ?

Solution :-

→ (3 + 5/x)(9 - 15/x + 25/x²) = 3

we can write LHS as ,

→ (3 + 5/x){3² - 3 * (5/x) + (5/x)²} = 3

comparing LHS with (a + b)(a² - ab + b²) = a³ + b³ , we get,

• a = 3
• b = (5/x)

So,

→ (3)³ + (5/x)³ = 3

→ 27 + (125/x³) = 3

→ (125/x³) = 3 - 27

→ 125 = (-24)x³

→ x³ = (-125/24)

Now, we have to Find :-

→ (3 - 5/x)(9 + 15/x + 25/x²)

which can be written as ,

→ (3 - 5/x){3² + 3 * (5/x) + (5/x)²}

comparing with (a - b)(a² + ab + b²) = a³ - b³, we get,

→ (3)³ - (5/x)³

→ 27 - (125/x³)

Putting value of x³ Now,

→ 27 - {125/(-125/24)}

→ 27 - (-125 * 24) / 125

→ 27 - (-24)

→ 27 + 24

→ 51 (Ans.)

Also,

→ x³ = (-125/24)

or,

→ x³ = (-5) * (-5) * (-5) / (2 * 2 * 2 * 3)

→ x³ = (-5)³ / (2³ * 3)

cube root both sides,

→ x = (-5) / (2 * ³√3)

Or,

→ x = (-5) / {2 * (3)^(1/3)} . (Ans.)

Answer 2

Correct Question :- if (3+5/x)(9 - 15/x + 25/x²) = 3, then find the value of (3 - 5/x)(9+15/x+25/x²) and hence find x. ?

Solution :-

→ (3 + 5/x)(9 - 15/x + 25/x²) = 3

we can write LHS as ,

→ (3 + 5/x){3² - 3 * (5/x) + (5/x)²} = 3

comparing LHS with (a + b)(a² - ab + b²) = a³ + b³ , we get,

a = 3

b = (5/x)

So,

→ (3)³ + (5/x)³ = 3

→ 27 + (125/x³) = 3

→ (125/x³) = 3 - 27

→ 125 = (-24)x³

→ x³ = (-125/24)

Now, we have to Find :-

→ (3 - 5/x)(9 + 15/x + 25/x²)

which can be written as ,

→ (3 - 5/x){3² + 3 * (5/x) + (5/x)²}

comparing with (a - b)(a² + ab + b²) = a³ - b³, we get,

→ (3)³ - (5/x)³

→ 27 - (125/x³)

Putting value of x³ Now,

→ 27 - {125/(-125/24)}

→ 27 - (-125 * 24) / 125

→ 27 - (-24)

→ 27 + 24

→ 51 (Ans.)

Also,

→ x³ = (-125/24)

or,

→ x³ = (-5) * (-5) * (-5) / (2 * 2 * 2 * 3)

→ x³ = (-5)³ / (2³ * 3)

cube root both sides,

→ x = (-5) / (2 * ³√3)

Or,

→ x = (-5) / {2 * (3)^(1/3)} . (Ans.)