Question 103

If $$a=1+\sqrt{3},b=1-\sqrt{3}$$, then what is the value of $$(a^{2}+b^{2})$$ ?

Solution

Given : $$a=1+\sqrt{3}$$

Squaring both sides, => $$a^2=(1+\sqrt3)^2$$

=> $$a^2=1+3+2\sqrt3=4+2\sqrt3$$ ---------(i)

Similarly, $$b^2=4-2\sqrt3$$ ----------(ii)

Adding equation (i) and (ii), we get :

=> $$(a^2+b^2)=(4+2\sqrt3)+(4-2\sqrt3)=8$$

=> Ans - (B)

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