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2 years ago

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

Mathematics

1 answer:

3241004551 [841]2 years ago

5 0

Answer:

4.3 to 1 decimal place.

Step-by-step explanation:

x^3 - 5x - 59 = 0

Try x = 4.1:

f(4.1) = (4.1)^3 - 5(4.1) - 59 = -10.579

Try: 4.2:

f(4.2) = 4.2^3 - 5(4.2) - 59 = -5.912, Try x = 4.3:

f(4.3) = -0.993 (getting closer to 0!!)

f(4.4) = 4.184

NOTICE - there is a change of sign in the result so the root lies between 4.3 and 4.4.

Try x = 4.35:

f(4.35) = 1.563 so it looks like the root is closer to 4.3 than 4.4 because 1.563 is closer to zero than 4.184.

Just to double check let's calculate x = 4.32:

f(4.32) = 0.0216 - which is very close to zero.

So the answer is 4.3 to 1 decimal place.

(I've checked it out on my calculator - the root is 4.31958).

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Part B; Angle GRT' is a right angle.

Step-by-step explanation:

Part A:

From the given figure it is noticed that the vertices of the triangle are G(-6,5), R(-3,1) and T(2,6).

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