If a3 + b3 = 35 and ab = 6, then what is the value of a + b?
5
8
2
-8
A.
5
Let a + b = x
C.B.S.
(a + b)3 = a3 + b3 + 3ab(a + b)
⟹ x3 = 35 + 3 x 6 x (x)
⟹ x3 - 18x = 35
⟹ x(x2 - 18) = 5 x 7
check with the option,
Now,
⟹ x = 5, x2 -18 = 7
∴ a + b = 5
What is the sum of 11 terms of an arithmetic progression if the 4th term is 11 and the 7th term is -4?
-75
55
11
100
What is the reflection of the point (-1, 3), in the line x = -4?
(-7, -3)
(-7, 3)
(7, -3)
(7, 3)
The co-ordinates of the centroid of a Δ ABC are (1, -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3, -4) and (0, 5) respectively.
(0, 13)
(0, 5)
(0, -5)
(0, -13)
D and E are points on side AB and AC of Δ ABC. DE is parallel to BC. If AD : BD = 2 : 5 and area of Δ ABC is 98 cm2, what is the area (in cm2) of quadrilateral BDEC?
90 cm2
98 cm2
94 cm2
86 cm2