If  find a and b. from Mathematics Number Systems
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    Number Systems

    Multiple Choice QuestionsShort Answer Type

    141.

    If  find the value of straight x squared plus 1 over straight x squared.

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    142. Let ‘a’ he a rational number and ‘b’ be an irrational number. Is ‘ab’ necessarily an irrational? Justify your answer with an example.
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    143.

    If straight a equals fraction numerator 3 minus square root of 5 over denominator 3 plus square root of 5 end fraction space and space straight b space equals fraction numerator 3 plus square root of 5 over denominator 3 minus square root of 5 end fraction, find a2 - b2.


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    144.

    If straight x equals 3 plus 2 square root of 2 comma check whether straight x plus 1 over straight x is rational or irrational.

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    145.

    If fraction numerator 2 over denominator square root of 3 plus square root of 5 end fraction plus fraction numerator 5 over denominator square root of 3 minus square root of 5 end fraction equals straight a square root of 3 plus straight b square root of 5 comma find a and b.

    fraction numerator 2 over denominator square root of 3 plus square root of 5 end fraction plus fraction numerator 5 over denominator square root of 3 minus square root of 5 end fraction equals a square root of 3 plus b square root of 5 rightwards double arrow space space space fraction numerator 2 left parenthesis square root of 3 minus square root of 5 right parenthesis over denominator left parenthesis square root of 3 plus square root of 5 right parenthesis left parenthesis square root of 3 minus square root of 5 right parenthesis end fraction plus fraction numerator 5 over denominator square root of 3 minus square root of 5 end fraction space fraction numerator square root of 3 plus square root of 5 over denominator square root of 3 plus square root of 5 end fraction space equals a square root of 3 plus b square root of 5 rightwards double arrow space space space space fraction numerator 2 left parenthesis square root of 3 minus square root of 5 right parenthesis over denominator 3 minus 5 end fraction plus fraction numerator 5 left parenthesis square root of 3 plus square root of 5 right parenthesis over denominator 3 minus 5 end fraction space equals space a square root of 3 plus b square root of 5 rightwards double arrow space space minus left parenthesis square root of 3 minus square root of 5 right parenthesis minus 5 over 2 left parenthesis square root of 3 plus square root of 5 right parenthesis space equals space a square root of 3 plus b square root of 5 equals negative 7 over 2 square root of 3 minus 3 over 2 square root of 5 equals a square root of 3 plus b square root of 5 rightwards double arrow space a equals negative 7 over 2. space space space space space space b equals negative 3 over 2 space
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    146. Simplify the following by rationalising the denominators:

    fraction numerator 2 over denominator square root of 5 plus square root of 3 end fraction plus fraction numerator 1 over denominator square root of 2 plus square root of 3 end fraction minus fraction numerator 3 over denominator square root of 5 plus square root of 2 end fraction
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    147. Evaluate: fraction numerator square root of 5 plus square root of 2 over denominator square root of 5 minus square root of 2 end fraction comma given that square root of 10 equals 3.162.
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    148. Simplify the following into a fraction with rational denominator fraction numerator 1 over denominator square root of 5 plus square root of 6 minus 11 end fraction.
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    149. Prove that left parenthesis 3 minus square root of 7 right parenthesis squared is an irrational number.
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    150. Evaluate cube root of left parenthesis 343 right parenthesis to the power of negative 2 end exponent end root space space
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