Question

solve for 50 points​

Answer 1

given

a/b = b/c

=>b^2 =ac

to proof

a^2 + b^2 + c^2 = (a + b+ c)(a - b + c)

proof

LHS

a^2 + b^2 + c^2:

= (a+ b +c)^2 - 2( ab + bc+ ca)

= (a+ b+ c)^2 -2(ab + bc + b^2)

= (a+b+c)^2 - 2b(a+ b + c)

= (a+b+c)(a - b + c)

RHS

hence LHS = RHS

identity used

(a + b + C)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

Answer 2

Answer:

a²+ b²+ c² :

= (a+ b +c)² - 2( ab + bc+ ca)

= (a+ b+ c)²-2(ab + bc + b²)

= (a+b+c)²- 2b(a+ b + c)

= (a+b+c)(a - b + c)

RHS

hence LHS = RHS