Question

ans fastttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt

Answer 1

Step-by-step explanation:

a)x + y = 12

and,

xy = 14

so,

(x+y)² = x² + y² + 2xy

then, by substituting the values,

(12)² = x² + y² + 2(14)

144 = x² + y² + 28

x² + y² = 144 - 28

x² + y² = 116 ......Ans

Answer 2

$\huge\underline{ \underline{ \texttt{ANSWER:}}}$

• X²+Y²=172
• X-Y=12

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$\huge\underline{ \underline{ \texttt{EXPLANATION:}}}$

GIVEN:

• X+Y=12
• XY=14

TO FIND:

• X²+Y²
• X-Y

SOLUTION:

$\large \boxed {\blue{{\tt{ \bigstar(X+Y)²=X²+Y²-2XY}}}}$

$\tt \large : \implies \: \: (12)²=X²+Y²-2(14)$

$\tt \large : \implies \: \: 144=X²+Y²-28$

$\tt \large : \implies \: \: 144 + 28=X²+Y²$

$\underline{ \boxed { \orange{\tt \large : \implies \: \: 172=X²+Y² }}} \huge \: \checkmark$

----------------------------------

$\large \tt \pink {\bigstar(X-Y)²=X²+Y²-2XY}$

$\large \tt : \implies \: \: (X-Y)² = 172-2(14)$

$\large \tt : \implies \: \: (X-Y)² = 172-28$

$\large \tt : \implies \: \: (X-Y)² = 144$

$\large \tt : \implies \: \: X-Y= \sqrt{144}$

$\large \underline{ \boxed{ \large \tt \green{ : \implies \: \: X-Y= 12}}} \huge \: \: \checkmark$

MORE IDENTITIES TO KNOW:

$\tt \circ \: \: \: \: (X+Y)(X-Y)=X²-Y²$

$\tt \circ \: \: \: \: (X+Y)²=X²+Y²+2XY$

$\tt \circ \: \: \: \: (X-Y)²=X²+Y²-2XY$

$\tt \circ \: \: \: \: (X+A)(X+B)=X²+(A+B) X+AB$