Question

If a+b = 3 and ab = 2, find the values of:
i) a2- b2

Answer 1

Answer:

Square on both sides

A +b²=3²

A²+ b²+2ab = 9

A²+ b²+2*2= 9

A²+b²=9-4

A²+b²= 5

Answer 2

Answer:

The value of ( a^2 - b^2 ) = ± 3

Step-by-step explanation:

It is given that:

a+b = 3 ... equation (i)

and ab = 2 ... equation (ii)

We have to find the value of : a^2 - b^2

We know that;

${a}^{2} - {b}^{2} = (a + b) \: (a -b ) \: ...equation(iii)$

We know the value of (a+b); now to find the value of (a-b):

We may proceed with;

${(a - b)}^{2} = ( {a}^{2} - 2ab + {b) }^{2} \\ = ( {a}^{2} + 2ab + {b}^{2} ) - 4ab \\ = {( a+ b)}^{2} - 4ab \\ \\ so \: {(a - b)}^{2} = {( a+ b)}^{2} - 4ab \: ...equation(iv)$

Now putting the values of (a+b) and ab in equation (iv) we get the value of (a-b);

${(a - b)}^{2} = {(3)}^{2} - (4 \times (2)) \\ = 9 - 8 \\ = 1 \\ \\ ( a-b ) = \sqrt{1} \\ ( a-b ) = \pm 1$

So, we get ( a - b ) = ± 1

Hence we now can calculate the value of (a^2 - b^2) from equation (i);

${a}^{2} - {b}^{2} = (a + b) \: (a -b ) \\ = 3 \times ( \pm1) \\ = \pm3$

So finally we get ( a^2 - b^2 ) = ± 3