Question

if x² +1/x² =27 find the value of 3x³ + 5x - 3/x³- 5/x​

Answer 1

Answer:your anwer is here

Step-by-step explanation:420.05

Answer 2

Answer :

3x³ + 5x - 3/x³ - 5/x = 445

Solution :

• Given : x² + 1/x² = 27
• To find : 3x³ + 5x - 3/x³ - 5/x = ?

The expression 3x³ + 5x - 3/x³ - 5/x can be rewritten as ;

→ 3x³ + 5x - 3/x³ - 5/x

→ 3x³ - 3/x³ + 5x - 5/x

→ 3(x³ - 1/x³) + 5(x - 1/x)

→ 3(x - 1/x)[ x² + (1/x)² + x•(1/x) ] + 5(x - 1/x)

→ 3(x - 1/x)(x² + 1/x² + 1) + 5(x - 1/x)

Now ,

Let's find the value of x - 1/x , thus here we go :

We know that , (a - b)² = a² + b² + 2ab

Thus ,

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

=> (x - 1/x)² = x² + 1/x² - 2

=> (x - 1/x)² = 27 - 2

=> (x - 1/x)² = 25

=> x - 1/x = √25

=> x - 1/x = 5

Now ,

=> 3x³ + 5x - 3/x³ - 5/x

= 3(x - 1/x)(x² + 1/x² + 1) + 5(x - 1/x)

= 3•5•(27 + 1) + 5•5

= 15•28 + 25

= 420 + 25

= 445

Hence ,

3x³ + 5x - 3/x³ - 5/x = 445