Question

All multiples of 4,starting with 8, can be written as the difference of two perfect squares.
4×y=(x+y)skoyar -(x-y)skoyar
like this 24 can be written as
24=4×6=4×6×1
then 24=(6+1)skoyar -(6-1)skoyar =7skoyar -5skoyar
24=4×3×2
then 24=(3+2)skoyar -(3-2)skoyar =5skoyar -1skoyar
using this, write thr. following number also as the difference of two perfect square.
a)36
b)60​

Answer 1

SOLUTION

TO DETERMINE

The following number as the difference of two perfect square.

a) 36

b) 60

FORMULA TO BE IMPLEMENTED

We are aware of the algebraic formula that

$\sf{4ab = {(a + b)}^{2} - {(a - b)}^{2} }$

EVALUATION

a)

$\sf{36}$

$\sf{ = 4 \times 9 }$

$\sf{ = 4 \times 9 \times 1}$

$\sf{ = {(9 + 1)}^{2} - {(9 - 1)}^{2} }$

$\sf{ = {(10)}^{2} - {(8)}^{2} }$

b)

$\sf{ 60 }$

$\sf{ = 4 \times 15 }$

$\sf{ =4 \times 5 \times 3}$

$\sf{ = {(5 + 3)}^{2} - {(5 - 3)}^{2} }$

$\sf{ = {(8)}^{2} - {(2)}^{2} }$

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