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Permutation

If √5 + √16 +...

Question

If $\sqrt{5 + \sqrt{16 + 6 \sqrt{7 + 4 \sqrt{3}}}} = x \sqrt{a} + y \sqrt{b} + z \sqrt{c},$ where a < b < c (a, b, c are integers, b is smallest odd prime number and x, y, z are non-negative rational numbers), then $(\frac{x}{y + z})$ is equal to

यदि $\sqrt{5 + \sqrt{16 + 6 \sqrt{7 + 4 \sqrt{3}}}} = x \sqrt{a} + y \sqrt{b} + z \sqrt{c},$ जहाँ a < b < c (a, b, c पूर्णांक हैं, b सबसे छोटी विषम अभाज्य संख्या है तथा x, y, z अ-ऋणात्मक परिमेय संख्याएँ हैं), तब $(\frac{x}{y + z})$ बराबर है

A

\frac{3}{2}

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B

0

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C

3

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D

\frac{1}{2}

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Solution

The correct option is C 3

Solution

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Similar questions

Find the following products:

(i) (3x + 2y + 2z) (9x² + 4y² + 4z² − 6xy − 4yz − 6zx)

(ii) (4x − 3y + 2z) (16x² + 9y² + 4z² + 12xy + 6yz − 8zx)

(iii) (2ab − 3b − 2c) (4a² + 9b² +4c² + 6 ab − 6 bc + 4ca)

(iv) (3x − 4y + 5z) (9x² +16y²+ 25z² + 12xy −15zx + 20yz)

Expand the following

(1)

(2)

(3)

(4)

(5)

(6)

Q. If degree of the polynomials f(x) = x³^ay^bz²^c and g(x) = x^a y³^bz²^c are equal, then the degree of the polynomial

p (x) = x^{\frac{a}{2}} y^{\frac{b}{2}} z^{\frac{c}{2}},

where a, b and c are even natural numbers and x, y and z are non-zero real numbers, is

यदि बहुपदों f(x) = x³^ay^bz²^c तथा g(x) = x^a y³^bz²^c की घात समान हैं, तब बहुपद

p (x) = x^{\frac{a}{2}} y^{\frac{b}{2}} z^{\frac{c}{2}}

की घात कौनसी है जहाँ a, b व c सम प्राकृत संख्याएँ हैं तथा x, y व z अशून्य वास्तविक संख्याएँ हैं

(i) If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are equal then show that,

\frac{y - z}{a (b - c)} = \frac{z - x}{b (c - a)} = \frac{x - y}{c (a - b)}

\frac{x}{3 x - y - z} = \frac{y}{3 y - z - x} = \frac{z}{3 z - x - y}

x + y + z \neq 0

then show that the value of each ratio is equal to 1.

(iii) If

\frac{a x + b y}{x + y} = \frac{b x + a z}{x + z} = \frac{a y + b z}{y + z}

x + y + z \neq 0

\frac{a + b}{2}

\frac{y + z}{a} = \frac{z + x}{b} = \frac{x + y}{c}

\frac{x}{b + c - a} = \frac{y}{c + a - b} = \frac{z}{a + b - c}

\frac{3 x - 5 y}{5 z + 3 y} = \frac{x + 5 z}{y - 5 x} = \frac{y - z}{x - z}

then show that every ratio =

\frac{x}{y}

HCF of $x^{6} y^{4} z^{2}$ , $x^{5} y^{4} z^{6}$ and $x^{7} y^{9} z^{4}$ is $x^{a} y^{b} z^{c}$ . Then a-b-c+2 = ___

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