Question

product of two rationalising factors is -1.in those one factor is 2+√5.find the other​

Answer 1

Answer:

2 - √5

Step-by-step explanation:

Product of two rationalising factors is -1.

In those one factor is 2+√5.find the other

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let the other factor be x

$2+\sqrt{5} \times x =-1 \\\\ x=\frac{-1}{2+\sqrt{5} } \\\\ rationalising \ factor=2-\sqrt{5}$

$x=\frac{-1}{2+\sqrt{5} } \times \frac{2-\sqrt5}{2-\sqrt{5} } \\\\ x=\frac{-[2-\sqrt{5}]}{(2+\sqrt{5} )(2-\sqrt{5} )} \\\\ x=\frac{-2+\sqrt{5}}{2^2-\sqrt{5}^2} \\\\ x=\frac{-2+\sqrt{5} }{4-5} \\\\x=\frac{-2+\sqrt{5} }{-1} \\\\ x=2-\sqrt{5}$

the other factor = 2 - √5

Answer 2

Given:

• Products of two rationalize factor is =-1
• One factor = 2+√5

Solution :

Let the factor be s.

$\sf \: 2 + \sqrt{5} \times s = - 1 \\ \\ \sf \: s = \frac{ - 1}{2 + \sqrt{5} } \\ \\ rationalize \: \: the \: \: denominator...... \\ \\ \sf \: s = \frac{ - 1}{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} } \\ \\ \sf \: s = \frac{- 2 + \sqrt{5} }{ {(2)}^{2} - {( \sqrt{5} })^{2} } \\ \\ \sf \: s = \frac{ - 2 + \sqrt{5} }{4 - 5} \\ \\ \sf \: s = \frac{ - 2 + \sqrt{5} }{ - 1} \\ \\ \sf \: s = 2 + \sqrt{5}$

•°• Other factors is 2+√5