{"id":92927,"date":"2025-06-01T11:36:56","date_gmt":"2025-06-01T11:36:56","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92927"},"modified":"2025-06-01T11:36:56","modified_gmt":"2025-06-01T11:36:56","slug":"if-the-sum-of-a-real-number-and-its-reciprocal-is-equal-to-5-then-wha","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-the-sum-of-a-real-number-and-its-reciprocal-is-equal-to-5-then-wha\/","title":{"rendered":"If the sum of a real number and its reciprocal is equal to 5, then wha"},"content":{"rendered":"

If the sum of a real number and its reciprocal is equal to 5, then what is the sum of the squares of the number and its reciprocal ?<\/p>\n

[amp_mcq option1=”25″ option2=”24″ option3=”23″ option4=”22″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2021<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe sum of the squares of the number and its reciprocal is 23.
\n<\/section>\n
\nGiven the sum of a variable and its reciprocal, we can find the sum of their squares by squaring the given sum and utilizing the algebraic identity $(a+b)^2 = a^2 + 2ab + b^2$.
\n<\/section>\n
\nLet the real number be $x$. Its reciprocal is $1\/x$.
\nWe are given that the sum of the number and its reciprocal is 5:
\n$x + \\frac{1}{x} = 5$.
\nWe need to find the sum of the squares of the number and its reciprocal, which is $x^2 + \\frac{1}{x^2}$.
\nSquare both sides of the given equation:
\n$(x + \\frac{1}{x})^2 = 5^2$
\nUsing the identity $(a+b)^2 = a^2 + 2ab + b^2$, where $a=x$ and $b=1\/x$:
\n$x^2 + 2 \\cdot x \\cdot \\frac{1}{x} + (\\frac{1}{x})^2 = 25$
\n$x^2 + 2 \\cdot 1 + \\frac{1}{x^2} = 25$
\n$x^2 + 2 + \\frac{1}{x^2} = 25$
\nSubtract 2 from both sides:
\n$x^2 + \\frac{1}{x^2} = 25 – 2$
\n$x^2 + \\frac{1}{x^2} = 23$.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

If the sum of a real number and its reciprocal is equal to 5, then what is the sum of the squares of the number and its reciprocal ? [amp_mcq option1=”25″ option2=”24″ option3=”23″ option4=”22″ correct=”option3″] This question was previously asked in UPSC CISF-AC-EXE – 2021 Download PDFAttempt Online The sum of the squares of the … <\/p>\n

Detailed SolutionIf the sum of a real number and its reciprocal is equal to 5, then wha<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1089],"tags":[1110,1102],"class_list":["post-92927","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1110","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIf the sum of a real number and its reciprocal is equal to 5, then wha<\/title>\n<meta name=\"description\" content=\"The sum of the squares of the number and its reciprocal is 23. 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