Question

If (a+b)=7 and ab=10, find the value of (a-b)

a; 3
b; 11
c; 15
d; 8​

Answer 1

Answer:

(a) 3

Step-by-step explanation:

Given that,

(a+b) = 7

And

ab = 10

To find the value of (a-b)

We know that,

(a-b)^2 = a^2 -2ab + b^2

Resolving further, we get,

=> (a-b)^2 = a^2 +2ab + b^2 -2ab -2ab

But, we know that,

• a^2 + 2ab + b^2 = (a+b)^2

=> (a-b)^2 = (a+b)^2 - 4ab

Substituting the values, we get,

=> (a-b)^2 = 7^2 -4(10)

=> (a-b)^2 = 49 - 40

=> (a-b)^2 = 9

=> a-b = ±√9

=> a-b = ±3

Hence, the required Answer is (a) 3.

Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given that
• ( a + b ) = 7
• ab = 10

To Find:

• We have to find the value of ( a - b )

Solution:

We know that

$=> {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

Adding and subtracting 2ab on RHS

$=> {(a - b)}^{2} = ({a}^{2} + {b}^{2} - 2ab) + 2ab - 2ab$

$=>{(a - b)}^{2} = ({a}^{2} + {b}^{2} + 2ab) - 4ab$

We know that :

• ${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2b$

Using identity of ( a + b )²

$=>{(a - b)}^{2} = {(a + b)}^{2} - 4ab$

$=>{(a - b)}^{2} = {(7)}^{2} - 4(10)$

$=>{(a - b)}^{2} = 49 - 40$

$=>{(a - b)}^{2} = 9$

Taking square root on both sides

$=>(a - b) = \sqrt{9}$

$=> ( a - b ) = 3$

Hence option A is correct