​If $$\tfrac{1}{5\sqrt{\smash[b]{2}}-7}$$​ = $$a\sqrt{\smash[b]{2}}+b$$, then the value of a and b are: ​

Correct option is B

Given:

​$$\frac{1}{5\sqrt{2} - 7} = a\sqrt{2} + b$$

Solution:

Simplify, $$\frac{1}{5\sqrt{2} - 7}$$ multiply both numerator and denominator by the conjugate of the denominator $$5\sqrt{2}+7$$

$$\frac{1}{5\sqrt{2} - 7} \times \frac{5\sqrt{2} + 7}{5\sqrt{2} + 7} =\frac{5\sqrt{2} + 7}{(5\sqrt{2})^2 - (7)^2}$$ 

​​Simplify the denominator:

​$$(5\sqrt{2})^2$$ = 25×2=50 , $$7^2$$ = 49

​Denominator = 50 − 49=1

​$$\frac{5\sqrt{2} + 7}{1}$$ = $$5\sqrt{2}+7$$ 

​Compare with $$a\sqrt{2}+b$$​​

​$$a\sqrt{2}+b$$ = $$5\sqrt{2}+7$$ 

​a =5, b=7

Thus, correct answer is (b) 5,7