Question

Could someone please answer question number 25? Please answer only if u know (i don't appreciate jokes).best answer will be marked as brainliest

Answer 1

Step-by-step explanation:

Since b is a mean proportion between a and c.

Hence by geometric mean property:

${b}^{2} = ac \: \: ...(1) \\ LHS = \frac{ {a}^{4} + {a}^{2} {b}^{2} + {b}^{4} }{{b}^{4} + {b}^{2} {c}^{2} + {c}^{4} } \: \\ = \frac{ {a}^{4} + {a}^{2} \times ac + {(ac)}^{2} }{{(ac)}^{2} + ac \times {c}^{2} + {c}^{4} } \: \\ = \frac{ {a}^{4} + {a}^{3} c \: + {a}^{2} {c}^{2} }{{a}^{2} {c}^{2} + a {c}^{3} + {c}^{4} } \\ = \frac{ {a}^{2} ({a}^{2} + {a} c \: + {c}^{2} )}{ {c}^{2} ({a}^{2} + a {c} + {c}^{2} )} = \frac{ {a}^{2} }{ {c}^{2} } \\ = \: RHS \\ </p><p>THUS \: PROVED$