Question

⇔If x√75=y√45=z√15,then which of the following is true?
⇒x+y=2z
⇒x+y=3z
⇒x-y=2z
⇒x-y=3z
(HINT)-U MAY TAKE x√75=y√45=z√15=K
ФNEED COMPLETE EXPLANATIONФ
°U KNOW WHAT HAPPENS IF YOU SPAM!°

Answer 1

Given :  $\sqrt[x]{75} =\sqrt[y]{45} =\sqrt[z]{15}$

To Find : which of the statement is true ...

1. x+y=2z

2.x+y=3z

3.x-y=2z

4.x-y=3z

Solution:

$\sqrt[x]{75} =\sqrt[y]{45} =\sqrt[z]{15}$

$\implies \sqrt[x]{5\times 5\times3} =\sqrt[y]{3\times 3\times5} =\sqrt[z]{3\times 5}$

$\implies (5\times 5\times3)^{\frac{1}{x}} = (3\times 3\times5)^{\frac{1}{y}} = (3\times 5 )^{\frac{1}{z}}$

$\implies (5)^{\frac{2}{x}}(3)^{\frac{1}{x}} = (3)^{\frac{2}{y}} (5)^{\frac{1}{y}} = (3 )^{\frac{1}{z}} (5 )^{\frac{1}{z}}$

Equating 1st two terms

$(5)^{\frac{2}{x}}(3)^{\frac{1}{x}} = (3)^{\frac{2}{y}} (5)^{\frac{1}{y}}$

$(5)^{\frac{2}{x}-\frac{1}{y} } = (3)^{\frac{2}{y}-\frac{1}{x}}$

$(5)^{\frac{2y-x}{xy} } = (3)^{\frac{2x-y}{xy}}$

$(5)^{\frac{2y-x}{2x-y} } = 3$   Eq1

Similarly Equating 1st & 3 term

$(5)^{\frac{2z-x}{x-z} } = 3$    Eq2

Equating Eq1 and Eq2 and Equating powers of 5

( 2y - x ) /(2 x - y)  =  (2z - x)/(x - z)

=> 2xy - x² - 2yz + xz  = 4xz - 2x² - 2yz  + xy

=> x²  + xy   = 3xz

=> x + y = 3z

QED

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Answer 2

A computer is a machine that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming. Modern computers have the ability to follow generalized sets of operations, called programs. These programs enable computers to perform an extremely wide range of tasks.