Simple maths question please help :(?

Question

Using this example -> (p-q)^2 - p(p-2q) 
Using the format of the example, find the value of 21596^2 - 21600 x 21592 
Please show full workings, thank you so much, i will give you 10 points for your effort

love452 · Accepted Answer

21596^2 - 21600 x 21592
(p - q)^2 - p(p - 2q) 

---------

(p - q)^2 - p(p - 2q) 
= p^2 - 2pq + q^2 - p^2 + 2pq
= q^2

21,596 = 21,600 - 4
21,592 = 21,600 - 8 = 21,600 - 2(4)
p = 21,600
q = 4

21596^2 - 21600 x 21592
= (21,600 - 4)^2 - 21,600(21,600 - 2(4)) 
= 21,600^2 - 2(21,600)(4) + 4^2 - 21,600^2 + 2(21,600)(4)
= 4^2
= 16

---------

21596^2 - 21600 x 21592
= 16

Anonymous · Answer

(p - q)^2  - p(p-  2q) = (21600 - 4)^2 - 21600(21600 - 8) 
From above equation by comparing terms, p = 21600, q = 4
expand equation,
p^2 -2pq + q^2 - p^2 + 2pq =  q^2 = 16

Φ² = Φ+1 · Answer

(p-q)^2 - p(p-2q)
= (pÂ² - 2pq + qÂ²) - (pÂ² - 2pq)
= qÂ²

so here q = 21596 - 21592 = 4, so 21596^2 - 21600 x 21592  = qÂ² = 16

rephrased in more familiar terms xÂ² - (x+q)(x-q) = qÂ²

Comarsh · Answer

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Simple maths question please help :(?

4 Answers