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3 solutions
a^2 + 12 + 36 should be a^2 + 12a + 36 and a^2 + 2(2)(6) + 6^2 should be a^2 + 2(a)(6) + 6^2
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I used "a" for Abhay! :rage: :rage: :rage:
I am using x=1500 as approachment :) and the result is same
Let 1 4 9 7 = x then expression turns to:
⇒ ( x + 6 ) 2 + ( x − 3 ) 2 − ( x − 1 ) 2 − 2 x − 3 5
= x 2 + 1 2 x + 3 6 + x 2 − 6 x + 6 x − ( x 2 − 2 x + 1 ) − 2 x − 3 5
= x 2 + 6 x + 9
= ( x + 3 ) 2
Pluging 1 4 9 7 = x :
( x + 3 ) 2 = ( 1 4 9 7 + 3 ) 2 = ( 1 5 0 0 ) 2 = 2 2 5 0 0 0 0
You should have used n instead of x . :P
Let x = 1 4 9 6
1 5 0 3 2 + 1 4 9 4 2 − 1 4 9 6 2 − 2 × 1 4 9 7 − 3 5 = ( x + 7 ) 2 + ( x − 2 ) 2 − x 2 − 2 ( x + 1 ) − 3 5
1 5 0 3 2 + 1 4 9 4 2 − 1 4 9 6 2 − 2 × 1 4 9 7 − 3 5 = x 2 + 1 4 x + 4 9 + x 2 − 4 x + a − x 2 − 2 x − 2 − 3 5 = x 2 + 8 x + 1 6
Now as 1 4 9 6 = 1 5 0 0 − 4 substituting x = y − 4
1 5 0 3 2 + 1 4 9 4 2 − 1 4 9 6 2 − 2 × 1 4 9 7 − 3 5 = ( y − 4 ) 2 + 8 ( y − 4 ) + 1 6 = y 2 − 8 y + 1 6 + 8 y − 3 2 + 1 6
1 5 0 3 2 + 1 4 9 4 2 − 1 4 9 6 2 − 2 × 1 4 9 7 − 3 5 = y 2 − 3 2 + 3 2 = y 2
1 5 0 3 2 + 1 4 9 4 2 − 1 4 9 6 2 − 2 × 1 4 9 7 − 3 5 = 1 5 0 0 2 = ( 1 5 2 ) ( 1 0 0 2 ) = ( 2 2 5 ) ( 1 0 0 0 0 ) = 2 2 5 0 0 0 0
Let 1 4 9 4 = a then the expression changes to:
( a + 9 ) 2 + a 2 − ( a + 2 ) 2 − 2 ( a + 3 ) − 3 5
= a 2 + 1 8 a + 8 1 + a 2 − a 2 − 4 a − 4 − 2 a − 6 − 3 5
= a 2 + 1 2 a + 3 6
= a 2 + 2 ( 2 a ) ( 6 ) + 6 2
= ( a + 6 ) 2
= ( 1 4 9 4 + 6 ) 2
= ( 1 5 0 0 ) 2 = 2 2 5 0 0 0 0