Question

if a+b=4 and ab=-12,find a^2-b^2 ​

Answer 1

Answer:

a² - b² = ± 32

Step-by-step explanation:

⇒ a + b = 4

⇒ a = 4 - b   ... ( 1 )

Substituting this in another equation we get,

⇒ ab = -12

⇒ ( 4 - b ) ( b ) = -12

⇒ 4b - b² = -12

⇒ b² - 4b - 12 = 0

⇒ b² - 6b + 2b - 12 = 0

⇒ b ( b - 6 ) + 2 ( b - 6 ) = 0

⇒ ( b + 2 ) ( b - 6 ) = 0

⇒ b = -2, 6

Case 1: If b = -2

⇒ a = 4 - b

⇒ 4 - ( -2 ) = 4 + 2 = 6

Case 2: If b = 6

⇒ a = 4 - b = 4 - 6 = -2

Hence the numbers are 6 and -2.

⇒ a² - b² = ?

Case 1: a = 6 and b = -2

⇒ ( 6 )² - ( -2 )²

⇒ 36 - 4 = 32

Case 2: a = -2, b = 6

⇒ ( -2 )² - ( 6 )²

⇒ 4 - 36 = -32

Hence the answer for a² - b² can be ± 32 depending on the values of a and b.

Hope it helped !!

Thanks !!

Answer 2

Answer:

Step-by-step explanation:

Given that a+b= 4

a=4-b

To find the value of a^2-b^2

Put value of a in the equation

(4-b)^2-b^2

Use identity : (x-y)^2= x^2+y^2+2xy

=16 + b^2 + 2×4×b -b^2

=16+8b= 8(2+b)