Question

Show that: (p¼- q¼)(p¼ + q¼)(√P+√q)= p-q.​

Answer 1

See below ~

Explanation:

Identity used :

• (a - b)(a + b) = a² - b²

Simplifying the LHS :

• (p¼ - q¼)(p¼ + q¼)(√p + √q)
• (√p - √q)(√p + √q)
• p - q
• Equal to the RHS

∴ Hence, it is proved √

Answer 2

Explanation:

let p¼ = a, q¼ = b

L.H.S. = (a - b)(a + b)(a² + b²) = (a² - b²)(a² + b²) = (a²)² - (b²)² = p - q = R.H.S.