Question

The sum of a number and 6, multiplied by the sum of the number and 8 is equivalent to 17.

Answer 1

The sum of a number and 6, multiplied by the sum of the number and 8 is equivalent to 17.

(n + 6) (n + 8) = 17

n^2 + 14n - 31 = 0

Find the roots using quadratic equation

n = -15.94427191, 1.94427191

Substitute the roots in original equation n = -15.94427191

(-15.94+ 6) (-15.94 + 8) = 17

≈ 80 ≠ 17

The equation is not true.

Substitute n = 1.944 in original equation.

(-1.94+ 6) (-1.94 + 8) = 17

4.06 * 6.06 = 17

≈ 24.6036 = 17

The equation is not true.

Ths statement is false.

Comments

Step 1:

Let the number is n.

The sum of a number and 6 is n + 6.

Sum of the number and 8 is n + 8.

Product of these two sums is equivalent to 17 ⇒ (n + 6)(n + 8) = 17.

(n² + 6n +8n +48 ) = 17

n² + 14n + 48 = 17

n² + 14n + 48 -17 = 0

n² + 14n + 31 = 0

Find the roots using quadratic equation.

n = -2.757 and n = -11.242.

Check :

Consider  n = -2.757

(n + 6)(n + 8) = 17

= ( -2.757 + 6)( -2.757 + 8)

= ( 3.243)(5.243)

= 17.003049

Consider  n = -11.242.

(n + 6)(n + 8) = 17

= ( -11.242 + 6)( -11.242 + 8)

= ( -5.242)(-3.242)

= 16.994564

So the statement is true.

Solution :

n = -2.757 and n = -11.242.

The statement is true.

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Thanks for correcting me