Question

√15-√14/√15+√14= a- b√210. Find a and b.

Answer 1

Answer:

a = 29

b = 2

Step-by-step explanation:

Given that,

$\frac{ \sqrt{15} - \sqrt{14} }{ \sqrt{15} + \sqrt{14} } = a - b \sqrt{210}$

To find the values of a and b.

We need to rationalize the denominator.

Therefore, we will get,

$= > \frac{ \sqrt{15} - \sqrt{14} }{ \sqrt{15} + \sqrt{14} } \times \frac{ \sqrt{15} - \sqrt{14} }{ \sqrt{15} - \sqrt{14} } = a - b \sqrt{210} \\ \\ = > \frac{ {( \sqrt{15} - \sqrt{14}) }^{2} }{ {( \sqrt{15} )}^{2} - {( \sqrt{14} )}^{2} } = a - b \sqrt{210} \\ \\ = > \frac{ {( \sqrt{15} )}^{2} + {( \sqrt{14}) }^{2} - 2( \sqrt{15})( \sqrt{14} ) }{15 - 14} = a - b \sqrt{210} \\ \\ = > \frac{15 + 14 - 2 \sqrt{210} }{1} = a - b \sqrt{210} \\ \\ = > 29 - 2 \sqrt{210} = a - b \sqrt{210}$

Now, comparing the rational and irrational terms on the both sides, we have,

=> a = 29

=> b = 2

Hence, the required value of a = 29 and b = 2.