Question

Find 2p + 3q if 4p^2 + 9q^2 = 17 and 12pq = 8 . Given , p and q are both positive .

Answer 1

Application of Algebraic identity

Answer: Value of 2p + 3q = 5.

Explanation:

given that 4p² + 9q² = 17

And 12pq = 8 .

Need to find 2p + 3q

lets first modify given equation  4p² + 9q² = 17

=> (2p)² + (3q)² = 17 ---------eq(1)

using algebraic identity (a + b)² = a² + b² + 2ab

=>   a² + b²  =  (a + b)²  - 2ab

On applying modified algebraic identity on Left hand side of eq (1 ) , we get

(2p+ 3q)² - 2 × (2p) x ( 3q) = 17

=> (2p+ 3q)² - 12pq = 17

=>  (2p+ 3q)²  = 17 + 12pq

on substituting given value of 12pq = 8 in above equation we get

(2p+ 3q)²  = 17 + 8

=> (2p+ 3q)² = 25

=>2p+ 3q = √25

=>2p+ 3q = 5

Hence value of 2p + 3q = 5.

#answerwithquality

#BAL