Question

(12) If a+b=7 and ab= 6, find a²- b²​

Answer 1

Answer:

35 or -35

Step-by-step explanation:

Given that,

a + b = 7

And

ab = 6

To find the value of a²- b²

We know that,

a²- b² = (a+b)(a-b)

So, we need to find value of (a-b) first.

Now, we know that,

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

Therefore, substituting the values, we get,

$= > {7}^{2} = {(a - b)}^{2} + 4(6) \\ \\ = > {(a - b)}^{2} + 24 = 49 \\ \\ = > {(a - b)}^{2} = 49 - 24 \\ \\ = > {(a - b)}^{2} = 25 \\ \\ = > {(a - b)}^{2} = {( \pm5)}^{2} \\ \\ = > a - b = \pm5$

Therefore, we will get,

=> a²- b² = 7(+5) or 7(-5)

=> a²- b² = 35 or -35

Hence, the required value is 35 or -35.