myhelper: RD Sharma 2020 solution class 9 chapter 4 Algebraic Identities VSAQS

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RD Sharma 2020 solution class 9 chapter 4 Algebraic Identities VSAQS

VSAQS

Page-4.33

Question 1:

If x +

$\frac{1}{x}$ = 3, then find the value of

$x^{2} + \frac{1}{x^{2}}$ .

Answer 1:

We have to find the value of

Given

Using identity

Here

By substituting the value of

we get,

By transposing + 2 to left hand side, we get

Hence the value of

is

.

Question 2:

If

$x + \frac{1}{x} = 3$ , then find the value of

$x^{6} + \frac{1}{x^{6}}$ .

Answer 2:

We have to find the value of

Given

Using identity

Here

By substituting the value of

We get,

By transposing + 2 to left hand side, we get

Cubing on both sides we get,

Using identity

${(a + b)}^{3} = a^{3} + b^{3} + 3 a b (a + b)$
Here

Put

we get

By transposing 21 to left hand side we get ,

Hence the value of

is

.

Question 3:

If a + b = 7 and ab = 12, find the value of a² + b²

Answer 3:

We have to find the value of

Given

Using identity

By substituting the value of

we get

By transposing +24 to left hand side we get ,

Hence the value of

is

.

Question 4:

If a − b = 5 and ab = 12, find the value of a² + b².

Answer 4:

We have to find the value

Given

Using identity

By substituting the value of

we get ,

By transposing – 24 to left hand side we get

Hence the value of

is

.

Question 5:

If

$x - \frac{1}{x} = \frac{1}{2}$ , then write the value of

$4 x^{2} + \frac{4}{x^{2}}$

Answer 5:

We have to find the value of

Given

Using identity

Here

By substituting the value of

we get

By transposing – 2 to left hand side we get

By taking least common multiply we get

By multiplying 4 on both sides we get

Hence the value of

is

Question 6:

If

$a^{2} + \frac{1}{a^{2}} = 102$ , find the value of

$a - \frac{1}{a}$ .

Answer 6:

We have to find the value of

Given

Using identity

Here

By substituting

we get

Hence the value of

is

Question 7:

If a + b + c = 0, then write the value of

$\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b}$

Answer 7:

We have to find the value of

Given

Using identity

Put

Hence the value of

is

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