Question

The equation x^3-5x=59 has a solution between 4and 5 . Use trail and improvement method. Give your answer to 1 decimal place.

Answer 1

GiveN :

• The equation x³ - 5x = 59
• And it's solution lies between 4 and 5

To FinD :

• The Correct value of x

Solution :

If the solution lies between 4 and 5. Then we have to guess the number which satisfies the value of the equation.

So, take x = 4.2,4.3 and 4.4 and so on

$\rule{200}{2}$

Put Value of x = 4.2

⇒x³ - 5(x)

⇒(4.2)³ - 5(4.2)

⇒74.088 - 21

⇒53.008

• This value it too small then 59

$\rule{200}{2}$

Put Value of x = 4.3

⇒(4.3)³ - 5(4.3)

⇒79.507 - 21.5

⇒58.007

• This value is also smaller

$\rule{200}{2}$

Put Value of x = 4.4

⇒(4.4)³ - 5(4.4)

⇒85.184 - 22

⇒63.184

• This value is too much larger

$\rule{200}{2}$

As we move ahead from 4.4 the value increases. and if we will go backwards which is 4.1 then values decreases. So, the approximately value of x is coming after putting x = 4.3

➠ Value of x is 4.3