Given expression
= [(a + b )2 - (a - b )2] / ab
= 4ab/ab
= 4
where, a = 999, b = 588
Given expression
[a3 + b3 + c3 - 3abc] / [a2 + b2 + c2 - ab - bc - ca]
= a + b + c
= 0.5 + 0.2 + 0.3
where, a = 0.5, b = 0.2, c = 0.3
? = [5 -[3/4 + {21/2 - (1/2 + 1/6 - 1/7)}]]/2
= [5 - [3/4 + {5/2 -(1/2 + 7 - 6/42)}]]/2
= [5 - [3/4 + {5/2 - (1/2 + 1/42)}]]/2
= [5 - [3/4 + {5/2 - (21 + 1 /42)}]]/2
= [5 - [3/4 + {5/2 - 22/42}]]/2
= [5 - [3/4 + {105 - 22/42}]]/2
= [5 - [3/4 + 83/42]] / 2
= [5 - [63 + 166/84]]/2
= (191/84)/2
=191/168 = 123/168
We know that,
(a + b + c)2 = (a2 + b2 + c2) + 2(ab + bc + ca )
? 196 = 96 + 2(ab + bc + ca)
? 2(ab + bc + ca) = 196 - 96 = 100
? (ab + bc + ca) = 100/2 = 50
Since, a + b + c = 0
Then, a + b = -c ....(i)
a + c = -b .........(ii)
b + c = -a ....(iii)
Now, [(a + b)/c + (b + c)/a + (c + a)/b] x [a/(b + c) + b/(c + a) + c/(a + b)]
Now, putting the value of a + b , b + c and c + a from Eqs. (i), (ii) and (iii) , we get
[(-c)/c + (-a)/a + (-b)/b] x [a/-a + b/-b + c/-c]
[(-1) + (-1) + (-1)] [(-1) + (-1) + (-1)]
= (-3) x (-3) = 9
? a + 1/b = 1
ab + 1 = b ...(i)
Also, b + 1/c = 1
? b = 1 - 1/c ...(ii)
From Eqs. (i) and (ii), we get
ab + a = 1 - 1/c
? ab = -1/c
? abc = -1
Given expression
= [(a + b)2 + (a - b)2] / [a2 + b2]
= 2(a2 + b2) / (a2 + b2)
= 2
where, a = 238, b = 131
?7 / (4 + ?2) = [7 / (4 + ?2)] x [(4 - ?2 ) / (4 - ?2]
= 7(4 - ?2) / (16 - 2)
[? (a + b)(a - b) = a2 - b2]
= 7(4 - ?2 )/14
= (4 - ?2)/2
= (4 - 1.4142)/2
= 2.5858/2 = 1.2929
(0.96)3 - (0.1)3/ [(0.96)3 + 0.096 + 0.01]
= (0.96)3 - (0.1)3 = (0.96 - 0.1) [(0.96)2 + 0.96 x 0.1 + (0.1)2]
[? a3 - b3 = (a - b) (a2 + ab + b2)]
= (0.96 - 0.1) [(0.96)2 + 0.096 + 0.01]/(0.96)2 + 0.096 + 0.01
= 0.96 - 0.1 = 0.86
? = 32/3 + 23/4 + 11/2
= 3 + 2 + 1 + (2/3 + 3/4 + 1/2)
= 6 + (8 + 9 + 6)/12 = 6 + (23/12)
= 6 + (111/12) = 711/12
(?)1/2 = (5568 ÷ 87)1/3 + (72 x 2)1/2
= (64)1/3 + (144)1/2
? ? = (4 + 12)2 = 256
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