Question

if a+b = 4 and ab = -12 find a2-b2.​

Answer 1

${\pink{\bf{\huge{\star{Smile{\star}}}}}}$

a+b=4

a=4-b---(2)

ab=-12

(4-b)b=-12

$4b - {b}^{2} = - 12 \\ {b}^{2} - 4b - 12 = 0 \\ {b}^{2} - 6b + 2b - 12 = 0 \\ b(b - 6) + 2(b - 6) = 0 \\ (b + 2)(b - 6) = 0 \\ b = - 2 \: and \: b = 6$

let us take b as 6 now substitute in eq (2)

a=4-b

a=4-6

a=-2

now finding the value of

${a}^{2} - {b}^{2}$

we know that,

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

substitute the values of a and b on the RHS,

$( - 2 + 6)( - 2 - 6) \\ 4 \times - 8 \\ = - 32$

therefore the value is

${\boxed{\boxed{\blue{\huge{\bold{-32}}}}}}$

Answer 2

First of all, what can we do with numbers. No more fear to numbers, letus play with numbers. But for playing with them, we need certain formulas to keep in our mind lifelong.

Well, First of all what I am going to do?

I should write the given informations.

[1] a+b = 4

Or, a²+2ab+b² = 16

Or, a²-24+b² = 16

Or, a²+b² = 40

[2] ab = - 12

Now, (a-b)² = a²-2ab+b² = 40+24 = 64

Therefore, (a-b) = √64 = 8

Now, The exact formula to be used in

this case is as follow :

a² - b² = (a+b) (a-b)

Or, a² - b² = 4×8

Or, a² - b² = 32

Thus, 16 is your required answer.