9:{"metadata":[["$","title","0",{"children":"iimkbmsat0025 - Say y = 3sqrt(2) - 4, find y^2 + 1/y^2. | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined Given: y = 3sqrt(2) - 4 We need to find: y^2 + 1y^2

We'll use the identity: y^2 + 1y^2 = (y + 1y)^2 - 2 This saves us from messy calculations with irrational expressions.

First, <=t's find 1y: 1y = 13sqrt(2) - 4 To rationalize, multiply by 3sqrt(2) + 43sqrt(2) + 4: 1y = 3sqrt(2) + 4(3sqrt(2) - 4)(3sqrt(2) + 4) Using (a-b)(a+b) = a^2 - b^2: Denominator = (3sqrt(2))^2 - 4^2 = 18 - 16 = 2 So: 1y = 3sqrt(2) + 42

Now calculate y + 1y: y + 1y = (3sqrt(2) - 4) + 3sqrt(2) + 42 = 3sqrt(2) - 4 + 3sqrt(2)2 + 2 = 3sqrt(2) + 3sqrt(2)2 - 2 = 6sqrt(2) + 3sqrt(2)2 - 2 = 9sqrt(2)2 - 2 = 9sqrt(2) - 42

Calculate the final answer: y^2 + 1y^2 = (y + 1y)^2 - 2 = (9sqrt(2) - 42)^2 - 2 = (9sqrt(2) - 4)^24 - 2 Using (a-b)^2 = a^2 - 2ab + b^2: (9sqrt(2) - 4)^2 = (9sqrt(2))^2 - 2(9sqrt(2))(4) + 4^2 = 162 - 72sqrt(2) + 16 = 178 - 72sqrt(2) Therefore: y^2 + 1y^2 = 178 - 72sqrt(2)4 - 2 = 178 - 72sqrt(2) - 84 = 170 - 72sqrt(2)4 Final Answer: 170 - 72sqrt(2)4"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"IIM-K (BMSAT),QA,Algebra,Identities"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"iimkbmsat0025 - Say y = 3sqrt(2) - 4, find y^2 + 1/y^2. | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined Given: y = 3sqrt(2) - 4 We need to find: y^2 + 1y^2

We'll use the identity: y^2 + 1y^2 = (y + 1y)^2 - 2 This saves us from messy calculations with irrational expressions.

Now calculate y + 1y: y + 1y = (3sqrt(2) - 4) + 3sqrt(2) + 42 = 3sqrt(2) - 4 + 3sqrt(2)2 + 2 = 3sqrt(2) + 3sqrt(2)2 - 2 = 6sqrt(2) + 3sqrt(2)2 - 2 = 9sqrt(2)2 - 2 = 9sqrt(2) - 42

Calculate the final answer: y^2 + 1y^2 = (y + 1y)^2 - 2 = (9sqrt(2) - 42)^2 - 2 = (9sqrt(2) - 4)^24 - 2 Using (a-b)^2 = a^2 - 2ab + b^2: (9sqrt(2) - 4)^2 = (9sqrt(2))^2 - 2(9sqrt(2))(4) + 4^2 = 162 - 72sqrt(2) + 16 = 178 - 72sqrt(2) Therefore: y^2 + 1y^2 = 178 - 72sqrt(2)4 - 2 = 178 - 72sqrt(2) - 84 = 170 - 72sqrt(2)4 Final Answer: 170 - 72sqrt(2)4"}],["$","meta","9",{"property":"og:url","content":"/iimk-bmsat-past-year-questions/2025/QA/19"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | JIPMAT Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"iimkbmsat0025 - Say y = 3sqrt(2) - 4, find y^2 + 1/y^2. | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined Given: y = 3sqrt(2) - 4 We need to find: y^2 + 1y^2

We'll use the identity: y^2 + 1y^2 = (y + 1y)^2 - 2 This saves us from messy calculations with irrational expressions.

Now calculate y + 1y: y + 1y = (3sqrt(2) - 4) + 3sqrt(2) + 42 = 3sqrt(2) - 4 + 3sqrt(2)2 + 2 = 3sqrt(2) + 3sqrt(2)2 - 2 = 6sqrt(2) + 3sqrt(2)2 - 2 = 9sqrt(2)2 - 2 = 9sqrt(2) - 42

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