If then
-
Solution
adding '1' to each term
⇒
-
Solution
∵ x +
⇒ 2x + ----------(1)
Cubing both sides of equation (1)
⇒
⇒ 8x3 +
⇒ 8x3+ = 18
The simplified form of term (x – y)3+ (y – z)3 + (z – x)3 is ?
-
Solution
Let x – y = a
y – z = b
z – x = c
If a + b + c = 0 then a3 + b3 + c3 = 3abc
So (x – y)3 + (y – z)3 + (z – x)3 = 3(x – y) (y – z) (z – x)
If where a ≠ b ≠ 0 then what will be the value of a3 + b3 ?
-
Solution
⇒ a2 + b2 = ab
⇒ a2 + b2 – ab = 0
Term a3 + b3 = (a + b) × (a2 + b2 –ab) = (a + b) × 0
So a3 + b3 = 0
If x2 + y2 + z2 + 2 = 2(y – x) then x4 – y3 + z2 = ?
-
Solution
x2 + y2 + z2 + 2 = 2 (y – x)
⇒ (x2 + 2x + 1) + (y2 – 2y + 1) + z2 = 0
⇒ (x + 1)2 + (y – 1)2 + (z – 0)2 = 0
⇒ x = – 1, y = 1, z = 0
Then x4 – y3 + z2 = (–1)4 – (1)3 = 0
If x2 + y2 + z2 = xy + yz + zx then
-
Solution
The only possible solution is x = y = z
So
=
For what value of K the equations x + 2y + 5 = 0 and 3x + ky + 15 = 0 have Infinite solution.
-
Solution
For Infinite solution, comparing multiples of x, y and constant term.
⇒ ⇒ k = 6
If then x = ?
-
Solution
∵
⇒
⇒ =
⇒ x =
⇒ x2 =
⇒ x =
If P = 99, then what will be value of P (P2 + 3P + 3) ?
-
Solution
∵ P = 99
term = P(P2 + 3P + 3)
= P[(P + 1)2 + (P+1) + 1]
= 99 [1002 + 100 + 1]
= 999,999
If then will be ?
-
Solution
......(i)
term
=