1c:I[1254,["7330","static/chunks/d3ac728e-78c3d5d7a486ed3a.js","5159","static/chunks/5159-48592f0bf1a47f9d.js","8175","static/chunks/8175-f84d59b9bd013e10.js","8167","static/chunks/8167-b25693a0140130f2.js","664","static/chunks/664-bceb0f356f9312eb.js","3703","static/chunks/app/practice-question/%5Bslug%5D/page-d1408559b663b83f.js"],"PracticeQuestionCard"] 1b:T4ae,{"@context":"https://schema.org","@type":"QAPage","name":"If a = 5 + 1 5 - 1 and b = 5 - 1 5 + 1 then the value of ( a^2 + ab +…","url":"https://vidyalelo.com/practice-question/simplify-if-a-frac-sqrt-5-1-sqrt-5-1-b-text-frac-sqrt-5-1-sqrt-5-1-then-the-value-of-89109","keywords":"practice questions, MCQ, MCQs with answers, objective questions, competitive exam questions, Competitive Exams, Competitive Exams MCQ, Competitive Exams MCQs, Competitive Exams questions, Competitive Exams practice questions, Aptitude, Aptitude MCQ, Aptitude MCQs, Aptitude questions, Aptitude practice questions, Surds And Indices","mainEntity":{"@type":"Question","name":"If a = 5 + 1 5 - 1 and b = 5 - 1 5 + 1 then the value of ( a^2 + ab +…","text":"If a = 5 + 1 5 - 1 and b = 5 - 1 5 + 1 then the value of ( a^2 + ab + b^2a^2 - ab + b^2 ) is = ?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"Option B. 4/3. Answer & Solution Answer: Option B Solution: & a + b = 5 + 1 5 - 1 + 5 - 1 5 + 1 & = ( 5 + 1 )^2 + ( 5 - 1 )^2 ( 5 - 1 ) ( 5 + 1 ) & = 2 [ ( 5 )^2 + 1 ]5 - 1 & = 2 ( 5 + 1 )4 & = 3 & a.b = 5 + 1 5 - 1 × 5 - 1 5 + 1 = 1 & Put value in expression & a^2 + ab + b^2a^2 - ab + b^2 & =…"}}}1d:T4f7,

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & a + b = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}} + \frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}} \cr & = \