Question

ifa+b=12and ab=32 than proved (a+2b)^2-5b^2=176

Answer 1

a + b = 12    (1)

ab = 32       (2)

Therefore, a = 32/b   (3)

Substitute by (3) in (1):

$32/b + b = 12\:\:\:\:(*b)\\32+b^2=12b\\b^2-12b+32=0\\(b-8)(b-4)=0\\b=8\:\:\:or\:\:\:b=4$.

Therefore,

a = 32/4    OR   a = 32/8

a = 8         OR    a = 4

Substitute in the given equation:

Choose a = 8, and b = 4:

$(a+2b)^2-5b^2=(8+2(4))^2-5(4)^2=176$

Answer 2

Answer:

Step-by-step explanation:

(a-b)^2= (a+b)^2-4ab

          =(12)^2-4x32    [as a+b=12 and ab=32]

          =144-128

          =16

or, (a-b)^2=16

so, a-b=4 [square root]

L.S=

(a+2b)^2-5b^2

=a^2 + 2xax2b + 4b^2 - 5b^2

=a^2 + 4ab - b^2

=a^2 - b^2 + 4ab

=(a+b)(a-b) + 4ab

=12x4 + 4x32

=48 + 128

=176

=R.S [Proved]