Q6 of 157 Page 22

Show that

(3x + 7)2 – 84x = (3x – 7)2

Solving L.H.S. first,


(3x + 7)2 – 84x


We know that


(a+ b)2 = a2 + b2 + 2a×b


⇒ (3x + 7)2 – 84x = ((3x)2 + (7)2 + 2×3x×7) – 84x


⇒ (3x + 7)2 – 84x = 9x2 + 49 + 42x – 84x


⇒ (3x + 7)2 – 84x = 9x2 + 49 – 42x


⇒ (3x + 7)2 – 84x = ((3x)2 + (7)2 – 2×3x×7)


Using (a– b)2 = a2 + b2 – 2a×b


⇒ (3x + 7)2 – 84x = (3x – 7)2


∵ L.H.S. = R.H.S.


Hence, proved.


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