Which of the following relations is/are true? I. \sqrt{7}+\sqrt{3}>\sqrt{5}+\sqrt{5} II. \sqrt{5}+\sqrt{5}>\sqrt{2}+\sqrt{8} III. \sqrt{5}+\sqrt{5}>\sqrt{7}+\sqrt{3}

Question 102

Which of the following relations is/are true?

I. $$\sqrt{7}+\sqrt{3}>\sqrt{5}+\sqrt{5}$$

II. $$\sqrt{5}+\sqrt{5}>\sqrt{2}+\sqrt{8}$$

III. $$\sqrt{5}+\sqrt{5}>\sqrt{7}+\sqrt{3}$$

Solution

The sum of (7,3), (5,5) and (2,8) is 10

Thus, squaring all the terms we get : $$(\sqrt7+\sqrt3)^2=10+2\sqrt{21}$$

$$(\sqrt5+\sqrt5)^2=10+2\sqrt{25}$$

and $$(\sqrt2+\sqrt8)^2=10+2\sqrt{16}$$

$$\because$$ First term is same (10) in all, thus $$\sqrt{25}>\sqrt{21}>\sqrt{16}$$

$$\therefore$$ $$\sqrt{5}+\sqrt{5}>\sqrt{7}+\sqrt{3}>\sqrt2+\sqrt8$$

=> Ans - (B)

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