Question

if x^a =y^b =z^c and y^2 =xz Prove: b= 2ac/a+c​

Answer 1

Answer:

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Step-by-step explanation:

jeiriuryruriruf

Answer 2

Answer:

• Given

$x {}^{a} = y {}^{ b} = z {}^{c} \: \: \: and \: \: \:y {}^{2} = x z$

• To prove
• $b = \frac{2ac}{a + c}$
• Proof
• $x {}^{a} = y {}^{b} \\ x = y {}^{ \frac{b}{a} } \\ z {}^{c} = y {}^{b} \\ z = y {}^{ \frac{b}{c} } \\ xz = y {}^{ \frac{b}{a} } y {}^{ \frac{b}{c} } \\ xz = y {}^{ \frac{b}{a} + \frac{b}{c} } \\ xz = y {}^{ \frac{b(a + c)}{ac} } \\ y {}^{2} = y {}^{ \frac{b(a + c)}{ac} } \\ \: \frac{b(a + c)}{ac} = 2 \\ b = \frac{2ac}{a + c}$