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Number Systems

Short 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.

a = 0 and b = $square root of 2$
Then, ab = 0 x $square root of 2 equals 0$ which is rational.
Hence, 'ab' is not necessarily an irrational.

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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.