Question

$if \: x + y - z = 5 \: and \: {x }^{2} + {y}^{2} + \\ {z }^{2} = 62 \: then \: find \: the \: value \: of \\ xy - yz - zx$
Hey guys
Can youuuuuuuu solve this question
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Answer 1

Answer:

$\huge{\pink{\boxed{\green{\sf{xy-yz-zx=\frac{-37}{2}}}}}}$

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

$\: \: \: \: \: \: \: { \orange{given}} \\ {\pink{ \boxed{ \green{ x + y - z = 5}}}} \\ {\pink{ \boxed{ \green{ x ^{2} + y^{2} + z^{2} =62 }}}} \\ \\ {\blue{to \: find}} \\ {\purple{ \boxed { \red{xy - yz - zx = ?}}}}$

☆ According to given question

☆ We know the formula of (x+y-z)^2

$\to (x + y - z)^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2xy - 2yz - 2zx \\ \to -({5})^{2} = 62 + 2(xy - yz - zx) \\ \to 25 - 62 = 2(xy - yz - zx) \\ \to -37 = 2(xy - yz - zx) \\ \to xy - yz - zx = \frac{ - 37}{2} \\ { \pink{ \boxed { \green{\therefore{xy - yz - zx = \frac{ - 37}{2} }}}}}$

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