Question

6. If x - y = 7 and r? + y2 = 67 find the value of xy.​

Answer 1

$Given \: x - y = 7 \: --(1)$

$and \; x^{2} + y^{2} = 67 \: --(2)$

/* On squaring both sides of the equation (1) , we get */

$(x - y )^{2} = 7^{2}$

$\implies x^{2} + y^{2} - 2xy = 49$

$\implies 67 - 2xy = 49 \: [ From \: (2) ]$

$\implies - 2xy = 49 - 67$

$\implies - 2xy = -18$

$\implies xy = \frac{ -18}{-2}$

$\implies xy = 9$

Therefore.,

$\red{ Value \: of \: xy}\green { = 9}$

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Answer 2

$\red{\text{NOTE:- THE GIVEN QUESTION IS WRONG.}}$

✯.CORRECT QUESTION,

1. if x-y=7 and x²+y²=67 .then, find the value of xy.

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow x-y=7\:---equation\:1$

$\sf\dashrightarrow x^2+y^2= 67\:---equation\:2$

✯.IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\:(x^2-y^2)= x^2+y^2-2xy \:\: \star}}}$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow The\:value\:of\:xy$

$\large\underline\bold{SOLUTION,}$

$\sf\therefore\text{ taking equation one,}$

$\sf\dashrightarrow x-y=7$

$\sf\therefore\text{ squaring both sides.we get,}$

$\sf\dashrightarrow (x-y)^2=(7)^2$

$\sf\implies x^2+y^2-2xy=49\:--- from\:the\:given\:identity.$

$\sf\implies 67-2xy= 49 \:----\boxed{from\:given\:equation\:2.}$

$\sf\implies -2xy=49-67$

$\sf\implies -2xy=-18$

$\sf\implies xy= \dfrac{-18}{-2}$

$\sf\implies xy= \dfrac{\cancel{-}\:18}{\cancel{-}\:2}$

$\sf\implies xy= \dfrac{18}{2}$

$\sf\implies xy= \cancel\dfrac{18}{2}$

$\sf\implies xy=9$

$\large{\boxed{\bf{ \star\:\: xy=9\:\: \star}}}$

$\large\underline\bold{THE\:VALUE\:OF\:xy\:IS\:9}$

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