Question

if a+b = 3 and a-b = 1 then
the value of a2+ b2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The value of a²+ b² is 5

Given,

a+b = 3 and a-b = 1

To Find,

Find the value of a²+ b²

Solution,

According to the question, a+b = 3 and a-b = 1

a+b= 3.......(1)

a-b = 1 .......(2)

Now, to find the value of a²+b², first we need the value of ab.

For calculating the value of ab

We are adding equation 1 and equation 2.

so, (a+b)+(a-b) = 3+1

=> a+b+a-b = 4

+b &-b will be cut

=> 2a= 4

=> a = 2

if a= 2, putting the value of a in the equation 1

then we get, 2+b= 3

=> b= 1

so, the value of ab= 2×1 = 2

Now, Squaring both sides of equation 1

(a+b)²= 3²

=> a²+b²+ 2ab= 9 [ we know that, (a+b) ²= a²+b²+ 2ab]

=> a²+b² = 9-2ab

=> a²+ b²= 9- 2×2 [ because, ab= 2]

=> a²+ b² = 9-4

=> a² + b² = 5

Hence, the value of a²+ b² is 5

#SPJ3