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Show that. (i) (3x+7)^2-84x=(3x-7)^2 (...

Show that. (i) `(3x+7)^2-84x=(3x-7)^2` (ii) `(9p-5q)^2+180pq=(9p+5q)^2` (iii) `(4/3(m)-3/4(n))^2+2mn=16/9(m^2)+9/16(n^2)` (iv) `(4pq+3q)^2-(4pq-3q)^2=48pq^2` (v) `(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0`

Text Solution

Verified by Experts

(i) `L.H.S. = (3x+7)^2 -84x = 9x^2+49+42x - 84x = 9x^2+49-42x`
` = (3x)^2+(7)^2 - 2**3x**7 = (3x-7)^2 = R.H.S.`

(ii)`L.H.S. = (9p-5q)^2+180pq = (9p)^2+(5q)^2-90pq+180pq`
`=(9p)^2+(5q)^2+90pq = (9p)^2+(5q)^2+2(9p)(5q) `
`= (9p+5q)^2 = R.H.S.`

(iii)`L.H.S. = (4/3m-3/4n)^2 +2mn= (4/3m)^2+(3/4n)^2 - 2**(4/3m)**(3/4n)+2mn`
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