If the average of a and 1/a is M, then which of the following is the average of a² and 1/a²?

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a , 1/a എന്നിവയുടെ ശരാശരി M ആണ് . എങ്കിൽ താഴെപ്പറയുന്നവയിൽ a², 1/a² എന്നിവയുടെ ശരാശരി ഏതാണ് ?

AM² - 1

B2M² - 1

C3M² - 1

D4M² - 1

Answer:

B. 2M² - 1

Read Explanation:

a , 1/a എന്നിവയുടെ ശരാശരി M ( a + 1/a )/2 = M a + 1/a = 2M ( a + 1/a )² = a² + 1/a² + 2 (2M)² = a² + 1/a² + 2 a² + 1/a² = 4M² -2 a², 1/a² എന്നിവയുടെ ശരാശരി = ( a² + 1/a² )/2 = (4M² - 2)/2 = 2M² - 1

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