Question

Divide 10 into two parts such that the sum of their squares is 52​

Answer 1

Answer:

Step-by-step explanation:

10 is divided into 2 parts

1st part is x

2nd part is 10-x

x^2+(10-x)^2=52

x^2+100-20 x+x^2=52

2 x^2-20 x+100=52

2 x^2-20 x+48=0

x^2-10 x+24=0

x^2-6 x-4 x+24=0

x(x-6)-4(x-6)=0

(x-4)(x-6)=0

x=4,6

1st part is 4

2nd part is 6

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Answer 2

Answer:

4 and 6

Step-by-step explanation:

Let 10 be divided in 2 parts : x and y

so,

x+y=10

=>y=10-x   .....(1)

x²+y²=52   ....(2)

Putting value of y from (1) in (2), we get

x²+(10-x)²=52

=>x²+100+x²-20x=52

=>2x²-20x+100=52

=>2x²-20x+48=0

=>x²-10x+24=0

=>x²-4x-6x+24=0

=>x(x-4)-6(x-4)=0

=>(x-4)(x-6)=0

=> x-4=0 or x-6=0

=>x=4 or x=6

For x=4, y=10-4=6

For x=6, y=10-6=4

Hence, 4 and 6 are the required two parts.

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