Question

★50 points ★

solve 5th

Answer 1

Question : √(9 + √48 -√32 - √24) = √a - √b + 2

Solution :

Squaring on both sides,

=> We get,

9 + √48 - √32 - √24 = (√a - √b + 2)²

=> Solving L.H.S,

=> 9 + √(16*3) - √(16*2) - √4*6)

=> 9 + 4√3 - 4√2 - 2√6,

Now,

Simplifying R.H.S,

=> a + b + 4 + 2*2*√a + (2*2*(-√b)) + 2*√a*(-√b)

=> a + b + 4 + 4√a - 4√b - 2√(ab)

Comparing L.H.S and R.H.S,

We observe,

9 and (a+b+4) Are only numbers without root,

=> 9 = a+b+4

=> a+b = 5,

Also,
Comparing Like terms (On L.H.S and R.H.S)

(1) :

=> +4√3 = +4√a

=> a = 3,

(2) :

=> -4√2 = -4√b

=> b = 2,

(3) :

=> 2√6 = 2√(ab)

=> 6 = ab,

From all these, What we obtained are,
(1) a + b = 5,
(2) a*b = 6,
(3) a = 3,
(4) b = 2,

(3) and (4) satisfy (1) and (2),

Also, By taking a = 3, and b = 2, Satisfy both L.H.S and R.H.S,

So, Finally What we can say is a+b is 5,

Conclusion : There will be no Mathematical solution, Except By comparison,

Therefore : The value of a+b is 5 (3+2)

Hope you understand, Have a Great day,
Thanking you, Bunti 360 !.

Answer 2

√(9 + √48 -√32 - √24) = √a - √b + 2

Solution :

Squaring on both sides,

=> We get,

9 + √48 - √32 - √24 = (√a - √b + 2)²

=> Solving L.H.S,

=> 9 + √(16*3) - √(16*2) - √4*6)

=> 9 + 4√3 - 4√2 - 2√6,

Now,

Simplifying R.H.S,

=> a + b + 4 + 2*2*√a + (2*2*(-√b)) + 2*√a*(-√b)

=> a + b + 4 + 4√a - 4√b - 2√(ab)

Comparing L.H.S and R.H.S,

We observe,

9 and (a+b+4) Are only numbers without root,

=> 9 = a+b+4

=> a+b = 5,

Also,

Comparing Like terms (On L.H.S and R.H.S)

(1) :

=> +4√3 = +4√a

=> a = 3,

(2) :

=> -4√2 = -4√b

=> b = 2,

(3) :

=> 2√6 = 2√(ab)

=> 6 = ab,

From all these, What we obtained are,

(1) a + b = 5,

(2) a*b = 6,

(3) a = 3,

(4) b = 2,

(3) and (4) satisfy (1) and (2),

Also, By taking a = 3, and b = 2, Satisfy both L.H.S and R.H.S,

So, Finally What we can say is a+b is 5,

Conclusion : There will be no Mathematical solution, Except By comparison,

Therefore : The value of a+b is 5 (3+2)