Question

Find the value of y from the equation =

(y+1) square - (y-4) square

= -55.

Hint : Use the identity
(a+b) (a-b) = a square

-b square​

Answer 1

Step-by-step explanation:

(y^2+2y +1)-(y^2-8y+16)=-55

y^2-y^2+2y+8y+1-16=-55

10y-15+55=0

5(2y-3+11)=0

2y-3+11=0

2y+9=0

y=-9/2

or

y=-4.5

Answer 2

Answer:

(y + 1)^2 - (y - 4)^2 = -55

using identity a^2 - b^2 = (a +b)(a-b)

Here a = y +1 and b = y - 4

therefore,

[ y + 1 ( y - 4 ) ] [ y + 1 - ( Y - 4 ) ] = -55

2y - 3 . 5 = -55

dividing both side by 5

2y - 3 = -11

2y = -8

y = - 4

VERIFICATION

( -4 + 1 )^2 - ( -4 -4 )^2 = -55

Taking L.H.S

( -4 + 1 )^2 - ( -4 -4 )^2

using identity a^2 - b^2 = (a + b) (a - b)

( -4 +1 -4 -4 ) ( -4 +1 +4 +4 )

-11 . 5

-55

Taking R. H. S.

-55

hence verified