2 0 ∗ 2 1 ∗ 2 2 ∗ 2 3 + 1 = ?
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From my point of view, I would prefer to put the A and it's equation first, THEN put A = 20, but that's just my preference. It's still fine if the one you state is your preference.
Great Solution, easy to understand and simple! How did you get from step 2 to step 3?
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A 4 + 6 A 3 + 1 1 A 2 + 6 A + 1
= A 4 + 3 A 3 + A 2 + 3 A 3 + 9 A 2 + 3 A + 3 A 2 + 3 A + 1 4
= ( A 2 + 3 A + 1 ) 2
20 * 21 22 23+1 = 212521 Root of 212521 is 461
Without a calculator?
20 * 21 * 22 * 23 + 1 = (20*23+1)^2
x(x+1)(x+2)(x+3)+1 = (x^2+3x+1)^2
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Here is my basic way: factoring. Let 2 0 = A
A ( A + 1 ) ( A + 2 ) ( A + 3 ) + 1
= A 4 + 6 A 3 + 1 1 A 2 + 6 A + 1
= ( A 2 + 3 A + 1 ) 2
⇒ A 2 + 3 A + 1
Purge A = 2 0 :
2 0 2 + 3 × 2 0 + 1 = 4 6 1