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If 𝒙 = 𝟓 − 𝟐√𝟔, find: 𝒙𝟐 + \frac{1}{^{x^2}}

Answer:

"hello friends welcome to lido learning
so the question on the screen is find
the value of x square plus 1 upon x
square
where x is equal to 5 minus 2 root 6
so if we know that x is equal to 5 minus
2 under root 6 first we'll calculate the
value of
1 upon x so 1 upon x
is 1 upon 5 minus 2
under root 6 now to rationalize the
denominator we will multiply
the numerator and denominator by the
conjugate of 5 minus 2 root 6
the conjugate of 5 minus 2 root 6 is 5
plus 2 root 6
and the denominator also is multiplied
by 5 plus 2 root 6
this results into 5 plus 2
under root 6 as the numerator and the
denominator
is in the form of a
minus b into a plus
b so a plus b into a minus b is a square
minus b square so a square minus b
square will be 5 whole square which is
25
minus 2 under root 6
whole square this will again
result into 5 plus 2 root seats remains
the same
in the numerator the denominator becomes
25
minus 2 root 6 whole square is 24
which is 25 minus 24 is 1 so the answer
comes out to be 5 plus 2 root 6
and this is 1 upon x that we had
calculated
now we will use an identity
x plus 1 upon x
whole square is equal to
it is into a plus b whole square form so
x square plus 1 upon
x square plus 2
so this is the identity that we are
going to use
so x plus 1 upon x so we know x is 5
minus 2 root 6
plus 1 upon x is 5 plus 2 root 6
5 plus 2 root
6 on the right hand side what do we get
x square plus 1 upon x square which is
what we have to find
so x square plus 1 upon x square we'll
keep it intact
and plus 2 so let us solve this
what do we get 2 root 6 gets cancelled
with minus 2 root 6 so
10 whole square
so 10 whole square minus 2
is equal to x square plus 1 upon x
square which we have to find
so 10 whole square is hundred hundred
minus two is
ninety eight so if you see
ninety eight is equal to x
square plus one upon x square which is
the
answer so the value is
98
so friends if you have any concerns
please write down below the video
and subscribe to the channel thank you"

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