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Fully explanation needed, 4 question 40 points .​

Answer 1

Question :-

11. The value of 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37.

a.) 237

b.) 126

c.) 56

d.) 64

12. The value of $\dfrac{(361)^{3} + (139)^{3} }{ {(361)}^{2} - 361 \times 139 + {(139)}^{2} }$

a.) 300

b.) 500

c.) 400

d.) 600

13. If x + y = 3, x² + y² = 5 then xy is

a.) 1

b.) 3

c.) 2

d.) 5

14. If x + 2 is a factor of x³ - 2ax + 16, then value of a is

a.) 3

b.) 1

c.) 4

d.) 2

Solution :-

In question 11, the concept of BODMAS is used. In BODMAS,

B - Brackets

O - Of (another word for multiplication)

D - Division

M - Multiplication

A - Addition

S - Subtraction

From ascending order sequence question will be solved.

11. 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37

First Multiplication part will be solved.

=> 31.6969 + 26.6862 + 5.6169

=> 64

Option d.) is correct.

$12. \: \: \: \dfrac{(361)^{3} + (139)^{3} }{ {(361)}^{2} - 361 \times 139 + {(139)}^{2} }$

Here, (361)³ + (139)³ is similar to a³ + b³ and (361)² - 361 × 139 + (139)² is similar to a² - ab + b².

$\tt{So, \dfrac{ {a}^{3} + {b}^{3} }{ {a}^{2} - ab + {b}^{2} } } \\ \\ \tt{=>\frac{(a + b){a}^{2} - ab + {b}^{2} }{{a}^{2} - ab + {b}^{2} }} \\ \\ \tt{ => (a + b)}$

As, a is 361 and b is 139.

a + b = 361 + 139 = 500.

Option b.) is correct answer.

13. Here, algebraic expression (a + b)² = a² + b² + 2ab is used.

In this question, x is a and y is b.

=> (x + y)² = x² + y² + 2xy

=>(3)² = 5 + 2xy

=> 9 = 5 + 2xy

=> 9 - 5 = 2xy

=> 4 = 2xy

$\tt{=> \dfrac{4}{2} = xy}$

=> 2 = xy

Option c.) is correct answer.

14. x + 2 is a factor of x³ - 2ax² + 16. It means that it will divide it fully leaving remainder 0.

=> x + 2 = 0

=> x = -2

f(x) = x³ - 2ax² + 16

f(2) = (2)³ - 2a × (2)² + 16

f(2) = 8 - 8a + 16

f(2) = - 8a + 24

As x + 2 is a factor, then f(2) = 0

=> 0 = -8a + 24

=> -24 = -8a

$\tt{=>\dfrac{-24}{8}= a}$

=> 3 = a

Option a.) is the correct answer.

Answer 2

$11) \: 5.63 \times 5.63 + 11.26 \times 2.37 + 2.37 \times 2.37$

$it \: can \: be \: written \: as \:$

$( {5.63)}^{2} + 2 \times 5.63 \times 2.37 + {(2.37)}^{2}$

$31.6969 + 26.6862 + 5.6169$

$64$

$so \: \: option \: d \: is \: the \: correct \: answer$

$12) \: \frac{ {(361)}^{3} + {(139)}^{3} }{ {(361)}^{2} - 361 \times 139 + {(139)}^{2} }$

$\frac{47045881 + 2685619}{130321 - 50179 + 19321}$

$\frac{49731500}{99463}$

$500$

$so \: the \: correct \: answer \: is \: option \: b$

$13) we \: need \: to \: find \: the \: value \: of \: xy$

$so \: we \: need \: to \: use \: {(x + y)}^{2}$

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

$now \: we \: have \: to \: put \: the \: values \: in \: the \: equation \:$

${(3)}^{2} = 5 + 2xy$

$9 - 5 = 2xy$

$4 = 2xy$

$xy = \frac{4}{2}$

$xy = 2$

$so \: the \: correct \: answer \: is \: option \: d$

$14) \: answer \: in \: the \: attachment$