Math, asked by pari200414, 10 months ago

Hyee guys. I need the answers fast and. Clearly explained. Plsssss. I have exams to morrow

If
$x = 9 - 4 \sqrt{5}$
Then find
$\frac{1}{x}$

pari200414: plsss answer this.

Answers

Answered by showkat718167

hi

x = 9 - 4√5

1/x = 1 / ( 9 - 4√5 )

=>

1/x = ( 9 + 4√5 ) /( 81 - 80)

=>

1/x = ( 9 +4√5 )

showkat718167: wait i will explain

showkat718167: Multiply numnator and denominator by 9 + 4√5

showkat718167: Then numnator comes 9 + 4√5

showkat718167: and denominator comes. ( 9 + 4√5 ) × ( 9 - 4√5 )

showkat718167: = 9² - ( 4√5 )² = 81 - ( 16 × 5 ) = 81 - 80 = 1

pari200414: ohhh. thanks.

showkat718167: becoz we know that ( a + b ) × ( a - b ) = a² - b²

pari200414: yah

showkat718167: if u found my ans quite helpful and errorless then plz mark it as brainlist ans

pari200414: yup

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