If 3-5-2-5-3-a-b-5- then the values of irrational numbers a and b are-3 Marks-

3+√(5)/2√(5)+3=(3+√(5)) (2√(5) 3)/(2√(5)+3)(2√(5) 3) nbsp; [1 Mark] =1+3√(5)/20 9 =1/11+3/11√(5) nbsp; nbsp;[1 Mark] Hence, a= 1/11 and b =3/11 nbs ...

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Byju's Answer

Standard IX

Mathematics

Rationalising Surds

If 3+√5/2√5+3...

Question

If $\frac{3 + \sqrt{5}}{2 \sqrt{5} + 3} = a + b \sqrt{5}$ , then the values of irrational numbers $a$ and $b$ are
[3 Marks]

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Solution

$\frac{3 + \sqrt{5}}{2 \sqrt{5} + 3} = \frac{(3 + \sqrt{5}) (2 \sqrt{5} - 3)}{(2 \sqrt{5} + 3) (2 \sqrt{5} - 3)} [1 M a r k] = \frac{1 + 3 \sqrt{5}}{20 - 9} = \frac{1}{11} + \frac{3}{11} \sqrt{5} [1 M a r k] Hence, a = \frac{1}{11} and b = \frac{3}{11}$
[1 Mark]

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If 3+√52√5+3=a+b√5, then the values of irrational numbers a and b are [3 Marks]

3+√52√5+3=(3+√5)(2√5−3)(2√5+3)(2√5−3)[1Mark]=1+3√520−9=111+311√5[1Mark]Hence, a=111 and b=311 [1 Mark]

If $\frac{3 + \sqrt{5}}{2 \sqrt{5} + 3} = a + b \sqrt{5}$ , then the values of irrational numbers $a$ and $b$ are
[3 Marks]

$\frac{3 + \sqrt{5}}{2 \sqrt{5} + 3} = \frac{(3 + \sqrt{5}) (2 \sqrt{5} - 3)}{(2 \sqrt{5} + 3) (2 \sqrt{5} - 3)} [1 M a r k] = \frac{1 + 3 \sqrt{5}}{20 - 9} = \frac{1}{11} + \frac{3}{11} \sqrt{5} [1 M a r k] Hence, a = \frac{1}{11} and b = \frac{3}{11}$
[1 Mark]