Question

2. Justify each step of the proof.

Conjecture: If 2(x2 + 5) = 60, then x is 5 or –5.

1. 2(x2 + 5) = 60                 1.

2. 2x2 + 10 = 60                  2.

3. 2x2 = 50                          3.

4. x2 = 25                            4.

5. x = ±5                              5.

Answer 1

Hello,

2(x²+5)=60
<==>x²+5=30 (divided teh 2 members by the positive 5 :keep the equality)
<==>x²-25=0 (substract 25 from 2 members)
<==>(x-5)(x+5)=0 (remarquable product a²-b²=(a+b)(a-b))
<==> x= 5 or x=-5 (a product if null if one at least of its factor is null)