In this article , some important algebra questions asked in SSC CGL previous year papers are discussed with explanations.
1. If
(i)
(ii)
(iii)
(iv)
Sol. Given .
Squaring both sides we get,
. Hence
(i) Now =
Putting , we get
=
=1
(ii) =
(iii) =
= =
(iv)
2. If , then find the value of
.
Sol. Cubing both the sides , we get
[
]
[ putting the value of
]
. Hence
OR
We can use the following formula directly
3. If then find the value of
.
Sol. Given
Adding 2 both sides we get . It can be written as
Taking +ve square root of both sides, we get
Again adding 2 both the sides we get
This implies . Hence
Now
=3 ( from equ. (i)
)
Thus
4. If then find the value of
.
Sol. To solve the above question you can use the following formula
(i ) If then
and
(ii) If then
Proof. (i ) Given
Squaring both sides we get
. Now subtracting 2 from both sides we get,
Similarly we can prove that If then
Now using the above formula the value of =
.
5. If , then find the value of
.
Sol. Dividing the given equation by , we get
. This implies
………… (i)
On squaring both sides we get, . It gives
………………. (ii)
Now cubing both sides of eqiuation (i), we get . This implies
…………….(iii)
squaring equation (ii) we get …………..(iv)
Now . This gives
. Thus
On putting the value of from (iii), the value of
6. If , then what is the value of
.
Sol. Given that .
Dividing by , we get
. Now squaring both sides we get
. This implies
.