If a > b are two real numbers such that a + b = 10 and a\u00b2 + b\u00b2 = 52, then what is the value of a – b ?<\/p>\n
[amp_mcq option1=”1″ option2=”2″ option3=”3″ option4=”4″ correct=”option2″]<\/p>\n
Now we need to find the value of $a-b$. We know the identity $(a-b)^2 = a^2 – 2ab + b^2$.
\nWe can rewrite this as $(a-b)^2 = (a^2 + b^2) – 2ab$.
\nSubstitute the values of $a^2+b^2$ and $ab$ that we found:
\n$(a-b)^2 = 52 – 2(24)$
\n$(a-b)^2 = 52 – 48$
\n$(a-b)^2 = 4$.
\nTaking the square root of both sides:
\n$a-b = \\pm \\sqrt{4} = \\pm 2$.
\nThe problem states that $a > b$, which means $a-b$ must be a positive value.
\nTherefore, $a-b = 2$.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"
If a > b are two real numbers such that a + b = 10 and a\u00b2 + b\u00b2 = 52, then what is the value of a – b ? [amp_mcq option1=”1″ option2=”2″ option3=”3″ option4=”4″ correct=”option2″] This question was previously asked in UPSC CISF-AC-EXE – 2021 Download PDFAttempt Online The value of $a – … <\/p>\n