What is the largest root of the equation $(x-1)^{2}=4x-7$

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godwin_ibrahimTyro

Asked: November 18, 20202020-11-18T20:33:02+00:00 2020-11-18T20:33:02+00:00In: Algebra

What is the largest root of the equation $(x-1)^{2}=4x-7$

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What is the largest root of the equation $(x-1)^{2}=4x-7$

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Sengemegz · Accepted Answer · 2020-12-17T20:32:31+00:00

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Sengemegz Moderator

2020-12-17T20:32:31+00:00Added an answer on December 17, 2020 at 8:32 pm

$(x-1)^{2}=4x-7$
$(x-1)(x-1)=4x-7$
$x^{2}-2x+1=4x-7$
$x^{2}-2x-4x+1+7=0$
$x^{2}-6x+8=0$
sum=-6
product=8
using factorization method
$\Rightarrow x^{2}-2x-4x+8=0$
$\Rightarrow x(x-2)-4(x-2)=0$
$\Rightarrow (x-2)(x-4)=0$
either $x-2=0 \therefore x=2$
or $x-4=0 \therefore x=4$

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What is the largest root of the equation $(x-1)^{2}=4x-7$