a =√5+√2/√5-√2. and b =√5-√2/√5+√2 then …

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a =√5+√2/√5-√2. and b =√5-√2/√5+√2 then find the value of a²+ab+b²/a²-ab+b²

Posted by Deshu Kaur 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Anshika Choudhary 9 months ago

a = (√5 + 2)/(√5 – 2) b = (√5 – 2)/( √5 + 2) Concept: First rationalize the values of ‘a’ and ‘b’ and then proceed. Formula used: (a + b)2 = a2 + b2 + 2ab (a + b)(a – b) = a2 – b2 Calculation: ∵ a = (√5 + 2)/(√5 – 2) ⇒ a = [(√5 + 2)( (√5 + 2)]/[(√5 – 2)(√5 + 2)] ⇒ a = [(√5 + 2)2]/[(√5)2 – (2)2] ⇒ a = [5 + 4 + 4√5]/(5 – 4) ⇒ a = (9 + 4√5) Similarly; b = (√5 – 2)/( √5 + 2) ⇒ b = [(√5 – 2)(√5 - 2)]/[(√5 + 2)(√5 – 2)] ⇒ b = [(√5 – 2)2]/[(√5)2 – (2)2] ⇒ b = [5 + 4 – 4√5]/(5 – 4) ⇒ b = (9 – 4√5) Now, a2 + b2 + ab = (a + b)2 – ab ⇒ (9 + 4√5 + 9 – 4√5)2 – [(9 + 4√5)( 9 – 4√5)] ⇒ (18)2 – [(9)2 – (4√5)2] ⇒ 324 – (81 – 80) ⇒ 324 – 1 ⇒ 323 ∴ The value of the given expression is 323.

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