Question

answer Question24 and explain it plzzz​

Answer 1

Answer:

545

Solution:

Given : x² + 1/x² = 27 ---------(1)

To find : 3x³ + 5x - 3/x³ - 5/x

Now,

We know that ,

( a - b)² = a² - 2ab + b²

Thus,

=> (x - 1/x)² = x² - 2•x•(1/x) + (1/x)²

=> (x - 1/x)² = x² - 2 + 1/x²

=> (x - 1/x)² = x² + 1/x² - 2

=> (x - 1/x)² = 27 - 2 { Using eq-(1) }

=> (x - 1/x)² = 25

=> x - 1/x = √25

=> x - 1/x = 5 -----------(2)

Also,

We know that ,

a³ - b³ = (a - b)(a² + ab + b²)

Thus,

=> x³ - (1/x)³ = (x - 1/x)•[x² + x•(1/x) + (1/x)²]

=> x³ - 1/x³ = (x - 1/x)•(x² + 1 + 1/x²)

=> x³ - 1/x³ = (x - 1/x)•(x² + 1/x² + 1)

=> x³ - 1/x³ = 5•(27 + 1)

{ Using eq-(1) and (2) }

=> x³ - 1/x³ = 5•28

=> x³ - 1/x³ = 140 ----------(3)

Now,

3x³ + 5x - 3/x³ - 5/x = 3x³ - 3/x³ + 5x - 5/x

= 3(x³ - 1/x³) + 5(x - 1/x)

{ using eq-(2) and (3) }

= 3•140 + 5•5

= 520 + 25

= 545

Hence,

The required value of

3x³ + 5x - 3/x³ - 5/x is 545 .

Answer 2

l thing your answere

Step-by-step explanation:

x^2+1/x^2=27

(x-1/X)^2=27-2=25

so,(x-1/x)=5

(x-1/X)^3=x^3&1/x^3-3xXx1/x(x-1/X)

5^3=x^3-1/x^3X5

125=x^3=1/x^3-1/x^3-5/X

3(x^3-1)x^3)+5(x-1/X)

3(x^3-1/x^3)+5(x-1/X)

3x140+5X5

420+25=445