In a set of 3 numbers the first is a positive integer, the second is 3 more than the first and the 3rd is a square of the second a) the first number in the set is x. write the second and third numbers in terms of x

b) the sum of the numbers is 77

c) write down an equation in terms of x

d) show that your equation simplifies to x²+8x-65=0

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Given:

In a set of 3 numbers the first is a positive integer, the second is 3 more than the first and the 3rd is a square of the second.

To find:

The equation for the given situation if the sum of the numbers is 77.

Solution:

a. Let the first number in the set is x.

The second is 3 more than the first. So, the second number is .

The 3rd number is a square of the second. So, the third number is .

Therefore, the first, second and third numbers are respectively.

b. The sum of the numbers is 77.

First number + Second number + Third number = 77

c. So, the equation in terms of x is:

Therefore, the required equation is .

d. On simplification, we get

Subtract 77 from both sides.

Therefore, the simplified form of the required equation is .

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step-by-step explanation: