Question

1. Let a and b be two positive real
numbers such that a√a + b√b=32 and a√b+b√a= 31. What is rhe value of 5(a+b)/7 ?​

Answer 1

Answer:

Answer:

9

Step-by-step explanation:

Given :

a√a + b√b = 32,

a√b + b√a = 31.

Solution :

a√a + b√b = 32  ...(1)

a√b + b√a = 31  ...(2)

let a = x² & b = y².

Then,

(1) can be re-written as,

⇒ (x)³ + (y)³ = 32 ....(3)

(2) can be re-written as,

⇒ x²y + xy² = 31 ...(4)

by adding  3×(4) + (3),

⇒ x³ + y³ + 3x²y + 3xy² = 32 + 31×3 = 125

⇒ (x + y)³ = 125

⇒ x + y = 5   ( ∵ -5 is not possible, as (-5)³ = -125 )

from (4)

⇒ x²y + xy² = 31,

⇒ x²y + xy² = xy(x + y) = 31

⇒ 5xy = 31

⇒  

⇒ a + b = x² + y² = (x + y)² - 2xy

=  

so,

Is this question from PRMO 2017 (I remember like solving this Q.)

Step-by-step explanation: