Check whether a÷b=b÷a where a=-3/2, b=7/6
Answers
Step-by-step explanation:
1. Multiply x
2
+ 4y
2
+ z
2
+ 2xy + xz – 2yz by (– z + x – 2y).
2. If a + b + c = 5 and ab + bc + ca = 10, then prove that a
3
+ b
3
+ c
3
–3abc = – 25.
3. Without actual division, prove that 2x4
– 6x3
+3x2
+3x – 2 is exactly divisible by
x
2
– 3x + 2.
4. Without actual division, prove that x3
– 3x2
– 13x + 15 is exactly divisible by
x
2
+ 2x – 3.
5. Find the values of a and b so that the polynomial x3
– 10x2
+ax + b is exactly divisible
by (x – 1) as well as (x – 2).
6. Divide the polynomial 3x
4
– 4x
3
– 3x –1 by x – 1.
7. Find the remainder obtained on dividing p(x) = x
3
+ 1 by x + 1.
8. Find the remainder when x
4
+ x
3
– 2x
2
+ x + 1 is divided by x – 1.
9. Check whether the polynomial q(t) = 4t
3
+ 4t
2
– t – 1 is a multiple of 2t + 1.
10. Check whether p(x) is a multiple of g(x) or not, where p(x) = x3
– x + 1, g(x) = 2 – 3x.
11. Using suitable identity, evaluate the following:
a. 1033
(ii) 101 × 102 (iii) 9992
12. Expand the following :
a. (4a – b + 2c)
2
b. (– x + 2y – 3z)
2
13. Factorise each of the following:
(i) 27y
3
+ 125z
3
(ii) 64m
3
– 343n
3
14. Factorise : 27x
3
+ y
3
+ z
3
– 9xyz
15. Without actually calculating the cubes, find the value of each of the following:
(i) (–12)3
+ (7)3
+ (5)3
(ii) (28)3
+ (–15)3
+ (–13)3
Answer:
a÷b ≠ b÷a
Step-by-step explanation:
a÷b = (-3/2) ÷(7/6)
(-3/2)×(6/7) = -18/14= -9/7
b÷a = (7/6) ÷ (-3/2)
= (7/6) × (-2/3) = (-14/18) = -7/9
a÷b ≠ b÷a