Math, asked by yugankreddy2007, 5 months ago

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

Answers

Answered by srudra0529
0

Answer:

geyeue7838

Step-by-step explanation:

jeiriuryruriruf

Answered by AdityaVishwakarma02
5

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}

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