In this article , some important algebra questions asked in SSC CGL previous year papers are discussed with explanations.

**1. If**

**then find**

(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 .