9514 1404 393
Answer:
3
Step-by-step explanation:
The radicals get in the way a bit, so we can define ...
x = √p
y = √q
Then the equation is ...
(x +y)/(1-x) = (4x+y)/(1-x^2)
Multiplying by (1-x^2), we have ...
(x +y)(1 +x) = 4x +y . . . . . . using 1-x^2 = (1-x)(1+x) the 1-x factor cancels
x^2 +xy +x +y = 4x +y . . . eliminate parentheses
x(x +y) = 3x . . . . . . . subtract (x+y)
x +y = 3 . . . . . . . . . . divide by x
This is the sum we're looking for:
√p +√q = 3
