Question

IF √X+Y=11 and X+√Y=7 find the value of x and y ?

Answer 1

√x + y = 7 x + √y = 11 Let √x = a and √y = b a + b² = 7 ---------- (1) a² + b = 11 ---------- (2) (1) × a² and (2) × a a³ + a²b² = 7a² ---------- (1) a² + ab = 11a ---------- (2) subtract a²b² – ab = 7a² – 11a ab(ab – 1) = a(7a – 11) b(ab – 1) = (7a – 11) ab² – b = 7a – 11 – b = 7a – ab² – 11 – b = a(7 – b²) – 11 a = (11 – b)/(7 – b²) Let b = 1, 2, ... when b = 2 a = (11 – b)/(7 – b²) = (11 – 2)/(7 – 4) = 9/3 = 3 so a = 3 and b = 2 √x = 3 and √y = 2 x = 9 and y = 4

Answer 2

Let √X =a or X=a^2

and √Y =b or Y =b^2
then

√X+Y=11 and X+√Y=7
a+b^2=11 and a^2+b=7

now solve