Square FUN

Algebra Level 1

Find 2 9 2 − 3 1 2 29^2 - 31^2 .

-124 -200 -120 -145 -310

Rigveda Gupta by Rigveda Gupta , 14, India

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3 solutions

Since a 2 − b 2 = ( a − b ) ( a + b ) ⟹ 2 9 2 − 3 1 2 = ( 29 − 31 ) ( 29 + 31 ) = − 2 × 60 = − 120 a^2 - b^2 = (a-b)(a+b) \implies 29^2 - 31^2 = (29-31)(29+31) = -2 \times 60 = \boxed{-120} .

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Lâm Lê
Nov 3, 2020

2 9 2 − 3 1 2 = 2 9 2 − ( 3 0 2 + 30 + 31 ) = 2 9 2 − ( 2 9 2 + 29 + 30 + 30 + 31 ) = 2 9 2 − 2 9 2 − 3 × 30 = − 120 29^2-31^2=29^2-(30^2+30+31)=29^2-(29^2+29+30+30+31)=\cancel{29^2}-\cancel{29^2}-3×30=-120

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Rigveda Gupta
Nov 1, 2020

29^2 - 31^2 = 29 + 31 x 2 = 120

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The absolute value is 120 but it should actually be 29^2 - 31^2 = -120. Perhaps you could edit the question so that the two terms are interchanged, I.e., 31^2 - 29^2.

A Former Brilliant Member - 7 months, 1 week ago

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