SOLUTION: if a, b belong to R+ such that {{{system(a*sqrt(a) + b*sqrt(b) = 183, a*sqrt(b) + b*sqrt(a) = 182)}}} then {{{(9/5)(a + b )= "?"}}}

SOLUTION: if a, b belong to R+ such that {{{system(asqrt(a) + bsqrt(b) = 183, asqrt(b) + bsqrt(a) = 182)}}} then {{{(9/5)(a + b )= "?"}}}

Question 1141270: if a, b belong to R+ such that

then
Answer by Edwin McCravy(20064) (Show Source): You can put this solution on YOUR website!

System 1:      

Let , ,  , , then



System 2:     

Multiply the 2nd equation by 3



Add the two equations:



Factor the left side:
 


Take cube roots of both sides:

Eq. 1     

Factor the left side of the 1st equation in system 2




Use Eq. 1 to substitute 9 for (x+y)


, reduce 183/9 to 61/3

Eq. 2     

Square both sides of Eq. 1:



Eq. 3     

Multiply Eq. 2 by -1 and add Eq. 3


 






Substitute  for xy in in Eq. 2







Since x²=a and y²=b,





Edwin

RELATED QUESTIONS
Show that: if a > 0, b > 0, and sqrt{a} < sqrt{b}, then a < b. Hint given: b - a (answered by math_tutor2020)

simplify a-b/sqrt a-sqrt... (answered by edjones)

{{{ (a-b)/(sqrt ( a )+sqrt ( b ))... (answered by josgarithmetic)

Let a, b, c, and d be distinct real numbers such that a = \sqrt{4 + \sqrt{5 + a}}, b =... (answered by CPhill,ikleyn)

Rationalize the denominator..... (answered by Fombitz)

find the value of A and B if sqrt(A) x sqrt(B) = 4 sqrt(A) - sqrt(B) =... (answered by stanbon)

(a) sqrt(10x) * sqrt(8x) (b) sqrt(24x^4) / sqrt(3x) (c) 5 /... (answered by Alan3354)

sqrt(a^2/b^5) sqrt (a/b sqrt... (answered by mananth)

sqrt () 18/ sqrt ()8 - sqrt 2 a) 9 sqrt () 2/6 b) 3 sqrt () 2 c) sqrt () 3... (answered by rapaljer)