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Question
Find the value of x if ∣∣
∣∣x−22x−33x−4x−42x−93x−16x−82x−273x−64∣∣
∣∣=0?
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Solution
Given ∣∣
∣∣x−22x−33x−4x−42x−93x−16x−82x−273x−64∣∣
∣∣=0Let△=∣∣
∣∣x−22x−33x−4x−42x−93x−16x−82x−273x−64∣∣
∣∣ApplyingC2=C2−2C1andC3=C3−3C1△=∣∣
∣∣x−212x−4−1−4x−8−11−40∣∣
∣∣ApplyingR2=R2−R1andR3=R3−R1△=∣∣
∣∣x−212−2−2−6−6−12−42∣∣
∣∣△=(−2)(−6)∣∣
∣∣x−212113127∣∣
∣∣△=12[(x−2)(7−6)−1(7−4)+1(3−2)]=12[x−2−3+1]=12(x−4)Given that △=0=>12(x−4)=0=>12x−48=0=>x=4
Given that △=0=>12(x−4)=0=>12x−48=0=>x=4
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