Math, asked by mehtasurbhi85, 10 months ago

x to the power 13 * y to the power 14 *(xy)to the power 5 *(xyz)to the power 12 / (xyz)to the power 4*(x)to the power10​

Answers

Answered by nagrenikita769
0

Step-by-step explanation:

a²+b⁴ = 47

Explanation:

Given: For a, b are real numbers such that a+b=3 and a^2+b^2=7a

2

+b

2

=7 .

Using Identities: a^4+b^4=(a^2+b^2)^2-2a^2\cdot b^2a

4

+b

4

=(a

2

+b

2

)

2

−2a

2

⋅b

2

[1]

First find the value of a^2b^2a

2

b

2

.

(a+b)^2=a^2+b^2+2a\cdot b(a+b)

2

=a

2

+b

2

+2a⋅b [2]

From the given condition, we have a+b=3 and a^2+b^2=7a

2

+b

2

=7 .

Substitute these values in equation [2], we have

(3)^2=7+2ab(3)

2

=7+2ab or

9=7+2ab

Simplify:

ab=1 or

a^2 \cdot b^2=1a

2

⋅b

2

=1

Now, to substitute the value of a^2 \cdot b^2=1a

2

⋅b

2

=1 and a^2+b^2=7a

2

+b

2

=7 in equation [1];

a^4+b^4=(7)^2-2\cdot 1=49-2=47a

4

+b

4

=(7)

2

−2⋅1=49−2=47

therefore, the value of a^4+b^4= 47a

4

+b

4

=47

Similar questions