Question

IF a= 7+4 root 3. find a power 3 + 1/a power 3

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Answer 1

Answered

If a=7-4 root 3 find the value of root a + 1/root a

1/a = 1/( 7 -4√3) = (7-4√3)/(7-4√3)(7+4√3)

=(7+4√3)/(49-48) = (7+4√3)

so, √a = √( 7 -4√3)

= √(2²+√3²-2.2√3)

=√(2 -√3)² = ( 2 -√3)

same way ,

1/√a = √(2² +√3² +2.2√3)

=√(2+√3)²

=(2 +√3)

now ,

√a + 1/√a = (2 -√3) + (2 +√3)=4