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Simplification

Theory and Formula



Question



Q1. Examine whether x - 1 is a factor of the polynomials. 4x3 - 5x2 - 2x + 3

(a) yes (b) no (c) can't say

Solution.
(a) yes
Solution

Q2. (256)1/4 ÷ 13/5 - 3 ÷ 5 = x, find x.

(a) 17 (b) 5 (c) 17/5 (d) 1/5

Solution.
{(4)4}1/4 x 1 - 3/5 = x

= 4 - 3/5

= 17/5
Solution

Q3. If one-tenth of square-root of x is 1. find x ?

Solution.
Let number is x
1/10
√x = 1
√x = 10
x = 100
Solution

Q4. If = 0.2319, then find the value of {(a2+2a + 1)1/2 - 1}.

Solution.
= {(a + 1)2}1/2 - 1

= a + 1 - 1

a = 0.2319
Solution

Q5. If x = (3)1/2 + 1/(3)1/2 -1 and y = 1/x so, find (x+y/x-y)2 .

Solution.
(x+y/x-y) = 2/(3)1/2
(x+y/x-y)2 = 4/3
Solution

Q6. If a = b = c, then find the value of
(a+b+c)2/ 3(a2+b2+c2)


(a) 1 (b) 2 (c) 3 (d) 4

Solution.
(3a)2/3(3a2) = (9a2)/(9a2) = 1
Solution

Q7. xm= yn= zp and y4 = x2z3 find n.

Solution.
xm= yn= zp = k (say)

x = k1/m, y = k1/n, z = k1/p

Now, y4 = x2z3

k4/n = k2/m.k3/p

4/n = 2/m + 3/p

4/n = (2p +3m)/mp

n = 4mp/(2p + 3m)
Solution

Q8. Reduce (4x+20)/(x2 - 25) to simplest form.
(a) 4/(x-5) (b) (x-5) (c) (x+5) (d) (x-5)/4

Solution.
4(x+5)/(x-5)(x+5) = 4/(x-5)
Solution

Q9. Find the value of
(x-y)2/(y-z)(z-x)
+
(y-z)2/(x-y)(z-a)
+
(x-z)2/(x-y)(y-z)


(a) 7 (b) 3 (c) 2 (d) 6

Solution.
(x-y)3/(x-y)(y-z)(z-x)
+
(y-z)3/(y-z)(x-y)(z-x)
+
(x-z)3 /(x-z)(x-y)(y-z)


(x-y)3+ (y-z)3 + (x-z)3/ (x-y)(y-z)(z-x)
=
3(x-y)(y-z)(z-x)/ (x-y)(y-z)(z-x)


= 3

Note : a3 + b3 + c3 = 3abc
if a + b + c = 0
Solution

Q10. If x + 1/x = (3)1/2, Find the value of x3 + 1/x3

Solution.
( x + 1/x)3 = {(3)1/2}3

x3 + 1/x3 + 3(3)1/2 = (3)3/2

x3 + 1/x3 = 0
Solution