Question

if x + y = 8 and xy = 3 3/4, find the values of
() X-y (i) 3(x2 + y2) (i) 5(x2 + y2) + 4(x - y).

Answer 1

Answer:

The values of the expressions are

$x-y=7\\\\3(x^{2} +y^{2} )=169.5\\5(x^{2} +y^{2} )+4(x-y)=310.5$

Step-by-step explanation:

Given value of the algebraic terms in two variables are

$x+y=8\\xy=3\frac{3}{4} =\frac{15}{4} = > y=\frac{15}{4x}$

Substituting the value of y in the above relation,we get

$x+\frac{15}{4x} =8= > 4x^{2} -32x+15=0\\= > x=7.5,0.5$

Hence the values of x and y can be considered as

$x=7.5\\y=0.5$

Now we shall solve the given expressions

(i) $x-y$

Substituting the values of the variables in above relation,we get

$x-y=7.5-0.5=7$

(ii) $3(x^{2}+ y^{2} )$

Substituting the values of the variables in above relation,we get

$3(7.5^{2}+0.5^{2})=169.5$

(iii) $5(x^{2} +y^{2} )+4(x-y)$

Substituting the values of the variables in above relation,we get

$5(7.5^{2}+0.5^{2})+4(7.5-0.5)=310.5$

Hence,the values of the expressions are deduced as shown above

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