Question

please answer me to my question
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Answer 1

Answer:

(i) a=1,b=2

(ii) a=3,b=6

(iii) a=2,b=6

Step-by-step explanation:

(i) =[(√3-1)/(√3+1)]×[(√3-1)/(√3-1)]

=(√3-1)²/(√3²-1²)

=[3-2(√3)(1)-1²]/(3-1)

=(3-1-2√3)/2

=(2-2√3)/2

=1-2√3

→(√3-1)/(√3+1)=1-2√3=a-b√3

a=1,b=2

(ii) =[(4+√2)/(2+√2)]×[(2-√2)/(2-√2)]

=[4+√2(2-√2)]/[(2²)-(√2²)]

=(8+4√2+2√2-√2²)/(4-2)

=(8+6√2-2)/2

=(6+6√2)/2

=3+6√2

→(4+√2)/(2+√2)=3+6√2=a+b√2

a=3,b=6

(iii) =[(3+√2)/(3-√2)]×[(3+√2)/(3+√2)]

=(3+√2)²/(3²-√2²)

=[3²+2(3)(√2)+2]/(9-2)

=(9+6√2+2)/(9-2)

=(1+1+6√2)/(1-1)

=2+6√2

→(3+√2)/(3-√2)=2-6√2=a+b√2

a=2,b=6