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Write the following sets in the roaster form 

(i) D = {t | t3 = t, t ∈ R}

(ii) E = {w | =3, w ∈ R}

(iii) F = {x | x4 – 5x2 + 6 = 0, x ∈ R}

0 2 Views | Posted 4 months ago
Asked by Shiksha User

  • 1 Answer

  • V

    Answered by

    Vishal Baghel | Contributor-Level 10

    4 months ago

    (i)We  have,  D={t|t3=t,t∈R}∴                        t3=t⇒                  t3−t=0    ⇒t(t2−1)=0⇒t(t−1)(t+1)=0    ⇒     t=0,1,−1∴                 D={−1,0,1}(ii)We  have,  E={w|w−2w+3=3,  w∈R}∴                  w−2w+3=3⇒                w−2=3w+9    ⇒w−3w=9+2⇒                 −2w=11             ⇒w=−112∴                 E={−112}(iii)We  have,  F={x|x4−5x2+6=0,x∈R}∴                          x4−5x2+6=0⇒           x4−3x2−2x2+6=0         ⇒x2(x2−3)−2(x2−3)=0⇒              (x2−3)(x2−2)=0          ⇒x=±3,±2∴                 F={−3,−2,2,3}

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