Question

If a,b,c,d are in G.P , show that (a+b+c+d)²=(a+b)²+2(b+c)²+(c+d)²

Answer 1

Answer:

1

Secondary School Math 5 points

If a,b,c,d are in G.P., show that (b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2

Ask for details Follow Report 30.12.2017

Answers

abhi178

abhi178 Genius

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

Let a = p, b = pr , c = pr² and d = pr³

Now, LHS = (b - c)² + (c - a)² + (d - b)²

= (pr - pr²)² + (pr² - p)² + (pr³ - pr)²

=( p²r² + p²r⁴ - 2p²r³) + (p²r⁴ + p² - 2p²r²) + (p²r^6 + p²r² -2p²r⁴)

= p²r^6 - 2p²r³ + p²

= (pr³) -2(pr³)(p) + p²

= (pr³ - p)²

= (p - pr³)²

=(a - d)² = RHS