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solve 5th
Answers
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 !.
√(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)