The degree of the expression x-x10-x-x10 is

The correct option is A 5 (a+√(b))^n=^nC_0a^n+^nC_1a^1(√(b))^n 1+^nC_2a^2(√(b))^n 2+........+^nC_n(√(b))^n (a √(b))^n=^nC_0a^n ^nC_1a^1(√(b))^n 1+^nC_2 ...

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Byju's Answer

Standard XII

Mathematics

Order of a Differential Equation

The degree of...

Question

The degree of the expression $(x + \sqrt{x})^{10} + (x - \sqrt{x})^{10}$ is

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Solution

The correct option is A 5
$(a + \sqrt{b})^{n} =^{n} C_{0} a^{n} +^{n} C_{1} a^{1} (\sqrt{b})^{n - 1} +^{n} C_{2} a^{2} (\sqrt{b})^{n - 2} + . . . . . . . . +^{n} C_{n} (\sqrt{b})^{n}$

$(a - \sqrt{b})^{n} =^{n} C_{0} a^{n} -^{n} C_{1} a^{1} (\sqrt{b})^{n - 1} +^{n} C_{2} a^{2} (\sqrt{b})^{n - 2} + . . . . . . . . +^{n} C_{n} (\sqrt{b})^{n} (- 1)^{n}$

Hence
$(x + \sqrt{x})^{10} =^{10} C_{0} x^{10} +^{10} C_{1} x^{1} (\sqrt{x})^{9} +^{10} C_{2} x^{2} (\sqrt{x})^{8} + . . . . . . . . +^{10} C_{10} (\sqrt{x})^{10} - - - - - - - (1)$

$(x - \sqrt{x})^{10} =^{10} C_{0} x^{10} -^{10} C_{1} x^{1} (\sqrt{x})^{9} +^{10} C_{2} x^{2} (\sqrt{x})^{8} + . . . . . . . . +^{10} C_{10} (\sqrt{x})^{10} - - (2)$
Adding eq (1) and (2)

$(x + \sqrt{x})^{10} + (x - \sqrt{x})^{10} = 2 [^{10} C_{0} x^{10} +^{10} C_{2} x^{2} (\sqrt{x})^{8} +^{10} C_{4} x^{4} (\sqrt{x})^{6} +^{10} C_{8} x^{8} (\sqrt{x})^{2} +^{10} C_{10} (\sqrt{x})^{10}]$

$(x + \sqrt{x})^{10} + (x - \sqrt{x})^{10} = 2 [^{10} C_{0} x^{10} +^{10} C_{2} x^{6} +^{10} C_{4} x^{7} +^{10} C_{8} x^{9} +^{10} C_{10} x^{5}]$

Hence the degree is 10.

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The degree of the expression (x+√x)10+(x−√x)10 is

The degree of the expression $(x + \sqrt{x})^{10} + (x - \sqrt{x})^{10}$ is