Question

if a-b=6 and a²+b²=48 find ab​

Answer 1

Answer:

a + b =2

a = 2-b ……..(i)

also, ab = 2 …………….(ii)

substituting the value of (a) in equation (ii) we will have :-

(2 - b)b = 48

2b -b^2= 48

now we have a quadratic equation :-

b^2 - 2b - 48=0

now we will split -2b in such a way that on addition the result will be = -2b

also, an multiplication the product will be -48

this will be in the following way :-**#

-8b * 6b = -48b

now by spliting the quadratic equation we have:-

b^2 -8b +6b -48 =0

now by factorizing we have :-

b(b - 8) + 6(b - 8) = 0

(b+6)(b-8) = 0

b+6 = 0

b= -6

b - 8= 0

b=8

so the value of b can be 8 or -6

substituing the value of be in equation (i) we have :-

a + b = 2

a + 8 = 2

a = 2–8

a = -6

or

a -6 = 2

a = 2 + 6

a = 8

in this way value of a can be -6 or 8

so we can conclude that when value of b = 8 then a will be = -6, also when the value of b=-6 then the value of a will be = 8

hope it will help you .

thanks for reading .