If a2 + b2 + 4c2 = 2(a + b - 2c) - 3 and a, b, c are real, then the value of (a2 + b2 + c2) is
2
3
C.
a2 + b2 + 4c2 = 2(a + b - 2c) - 3
⟹ a2 + b2 + 4c2 = 2a + 2b - 4c - 3
⟹ (a2 - 2a + 1) + (b2 - 2b + 1) + (4c2 + 4c + 1) - 1 - 1 - 1 = -3
⟹ (a - 1)2 + (b - 1)2 + (2c + 1)2 = 0
Hence,
(a - 1) = 0 ⟹ a = 1
(b - 1) = 0 ⟹ b = 1
(2c + 1) = 0 ⟹ c =-1/2
A number x, when divided by 289 leaves 18 as the remainder. The same number when divided by 17 leaves y as a remainder. The value of y is
2
3
1
5
An equation of the form ax + by + c = 0, where, represents a straight line which passes through
(2, 4)
(0, 0)
(3, 2)
None of these
The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator. Find the fraction.
If G is the centroid of Δ ABC and Δ ABC = 48 cm2, then the area of Δ BGC is
8 cm2
16 cm2
24 cm2
32 cm2