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Selina Solutions Class 9 Mathematics Solutions for Exercise 1(C) in Chapter 1 - Chapter 1- Rational and Irrational Numbers

Question 12 Exercise 1(C)

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

Answer:

Selina Solutions CONCISE Maths - Class 9 ICSE chapter Chapter 1- Rational and Irrational Numbers Question 12 Solution image

Video transcript
"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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