Find-the-product-of-all-the-real-values-of-a-that-satisfies-the-equation-4-a-4-a-4-

Question Number 55756 by otchereabdullai@gmail.com last updated on 03/Mar/19

Find the product of all the real values

of a that satisfies the equation

4 ∣ a - 4 ∣=∣ a + 4 ∣

Answered by mr W last updated on 03/Mar/19

i f a ⩽ - 4 :

- 4 (a - 4) = - (a + 4)

\Rightarrow a = \frac{20}{3} > 0 \Rightarrow n o s o l u t i o n

i f - 4 < a ⩽ 4

- 4 (a - 4) = a + 4

\Rightarrow a = \frac{12}{5} = 2.4 \Rightarrow s o l u t i o n

i f 4 < a :

4 (a - 4) = a + 4

\Rightarrow a = \frac{20}{3} = 6.67 \Rightarrow s o l u t i o n

a l l s o l u t i o n s a r e :

a = \frac{12}{5} a n d \frac{20}{3}

\Rightarrow \frac{12}{5} \times \frac{20}{3} = 16

Commented by otchereabdullai@gmail.com last updated on 03/Mar/19

Thank you soo much Prof W