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Algebra Level 2

( 1234 × 1234 − 1233 × 1235 ) × 123456789 = ? \large (1234 \times1234 - 1233 \times 1235)\times 123456789 = \, ?


The answer is 123456789.

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Dilwar Ali Alvee by Dilwar Ali Alvee , 31, Bangladesh

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2 solutions

⇒ ( 1234 × 1234 − 1233 × 1235 ) × 123456789 \Rightarrow (1234×1234-\color{#D61F06}{1233}×\color{#3D99F6}{1235})×123456789

= [ 123 4 2 − ( 1234 − 1 ) ( 1234 + 1 ) ] × 123456789 =[1234^2-\color{#D61F06}{(1234-1)}\color{#3D99F6}{(1234+1)}]×123456789

= [ 123 4 2 − ( 123 4 2 − 1 2 ) ] × 123456789 =[1234^2-(\color{#D61F06}{1234^2}-\color{#3D99F6}{1^2})]×123456789

⇒ 1 × 123456789 = 123456789 \Rightarrow 1×123456789=\color{#20A900}{\boxed{\color{magenta}{123456789}}}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Dilwar Ali Alvee
Feb 12, 2016

1×1-0×2 =1-0 =1 again, 2×2-1×3 =4-3 =1 and again, 10×10-9×11 =100-99 =1 so, we can see that, any real numbers square - multiplication of it's previous number and next number = 1(always) now, (1234×1234 -1233×1235) ×123456789 =1×123456789 =123456789 Ans:123456789

3 Helpful 0 Interesting 0 Brilliant 0 Confused

{(6789)(6789)} - {(6788) (6790)} (34567890)...?

Muhaimin Islam - 5 years, 4 months ago

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The answer of your question is 34567890.

Dilwar Ali Alvee - 5 years, 4 months ago

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