Question

X+y=15 and xy=56 find 2x+2y

Answer 1

Answer:

30

Step-by-step explanation:

x+y=15, xy=56

56=7x8

x=7 , y=8

2x+2y

=(2x7)+(2x8)

=14+16

30

Answer 2

required answer →

$\bold { \underline{ \underline \color{orange}{given}}} \orange→ \:$

x + y = 15 -------------(i)

xy = 56 -----------(ii)

$\bold { \underline{ \underline \color{orange}{answer}}} \orange→$

2x+2y = 30

$\bold { \underline{ \underline \color{orange}{solution}}} \orange→$

first way :-

we know that..

x + y = 15

now multiply 2 by both sides..

$\implies \: 2 \times (x + y) = 2 \times 15 \\ \\ \: \: \: \: \: \: →2x + 2y = 30$

second way :-

we know that.. x + y = 15

→ x = 15 - y .........(iii)

now substitute the value of x in eq.(ii)

$\implies \: (15 - y)y = 56 \\ \implies \: 15y - {y}^{2} = 56 \\ \implies \: {y}^{2} - 15y + 56 = 0$

it's form a quadratic equation

now we will solve the equation by Splitting the Middle term ;

$\: \: \: \: {y}^{2} - 15y + 56 \\ \\ →{y}^{2} + ( - 8 - 7)y + 56 = 0 \\ \\ → {y}^{2} - 8y - 7y + 56 = 0 \\ \\ → y(y - 8) - 7(y - 8) = 0 \\ \\ →(y - 7)(y - 8) = 0 \\ \\ \implies \: y - 7 = 0 \: \: or \: \: y - 8 = 0 \\ \\ \implies \: y = 7 \: \: or \: \: \: y = 8$

now substitute the value of 7 in eq.(iii)

→ x = 15 - 7 or x = 15 - 8

→ x = 8 or x = 7

so value of x can be 7 or 8

and same value of y also be 7 or 8

now put the value of x and y in 2x + 2y

$\implies \: (2 \times 7)+ (2 \times 8) \\→ \: 14 + 16 \\ → \: 30$

hence, 2x + 2y = 30