Question

If (x-y) =5

xy =16
then find x^2 +y^2 ​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• (x - y) = 5

• xy = 16

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• (x² + y²)

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

$\underline{\bigstar\:\textsf{A.T.Q:}}$

$\dashrightarrow\sf (x-y)=5\\\\{\scriptsize\qquad\bf{\dag}\:\:\texttt{Squaring Both Sides -}}\\\\\dashrightarrow\sf (x-y)^2=(5)^2\\\\\\\dashrightarrow\sf (x)^2+(y)^2-2xy=(5 \times 5)\\\\\\\dashrightarrow\sf x^2+y^2-(2 \times 16)=25\\\\\\\dashrightarrow\sf x^2+y^2-32=25\\\\\\\dashrightarrow\sf x^2+y^2=25+32\\\\\\\dashrightarrow\underline{\boxed{\sf x^2+y^2=57}}$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

⠀

$\therefore\:\underline{\textsf{Required Answer will be \textbf{57}}}.$

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Answer 2

ans:

Step-by-step explanation:

here , is a formula

(x-y)^2= x^2 +y^2 --2xy------------eq(1)

we have to put value here

from (a-b)^2 equation

x-y=5

sq both side

(x-y)^2=25

now, put value (x-y)^2

in eq(1)

25= x^2 +y^2 - 2(16) (xy=16)

25+32= x^2 +y^2

x^2 +y^2=57

hence proved