Robert the scientist

Algebra Level 2

Robert the scientist realised after conducting a few experiments, that if you get $2^{2}$ , and then get ( $2$ -1)( $2$ +1), $2^{2}$ will equal ( $2$ -1)( $2$ +1)+ 1. does $x^{2}$ equal ( $x$ -1)( $x$ +1)+1 for all real numbers $x$ ?

no yes

1 solution

Mikael Bashir
Jun 2, 2018

$x^{2}$ will always equal ( $x$ -1)( $x$ +1)+1. For example, if we substitute $x$ in the equation for 99, we will get that 9801 ( $99^{2}$ ) will equal to 9800+1 ((98 x 100)+1) . This happens because ( $x$ -1)( $x$ +1)+1 equals $x^{2}$ - $x$ + $x$ -1 +1, which simples down to $x^{2}$ , hence $x^{2}$ will always equal ( $x$ -1)( $x$ +1)+1

$(x+1)(x-1)+1=x(x-1)+1(x-1)+1=(x^2-x)+(x-1)+1=x^2-1+1=x^2$

X X - 3 years ago

Robert the scientist

1 solution

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