Can anyone help me out in this question?View attachment 54971
First expand (a+3√ 5)^2:- a^2+6a√ 5+45
Now the equation is:- a^2+6a√ 5+45+a-b√ 5=51
Taking √ 5 common:- a^2+a+45+(6a-b)√ 5=51
Now, we have to equate the integers on the left and right side:- a^2+a+45=51
Now, we have to equate the √ 5 coefficients on both sides:- 6a-b=0(It is equal to zero because there are no √ 5 coefficients on the right hand side)
(Note:-only equate the √5 coefficients after you have taken common, it is less likely that you will make errors)
Now solve the simultaneous equations
a^2+a+45=51----->1
6a-b=0----->2
a=2 or a=-3
b=12 or b=--18