Question

4. Find two consecutive even integers such that the square of the smaller is 10 more than the
larger.​

Answer 1

Answer:

4 and 6

Step-by-step explanation:

as they are even integers we take the integers as n,n+2

and it is given that   n²=n+2+10 which implies n²=n+12

so we get n²-n-12=0 so

n²-4n+3n-12=0 and n can take values 4 or  -3

but n is an even integer so the two integers are 4 and 6

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Answer 2

Answer:

4 and 6

Step-by-step explanation:

The two numbers:

2 n  and  2 n +  2

so we get:

( 2n)²  = ( 2 n  +  2 )  +  10

=  4 n  ² =  2 n  +  2  + 10

=  4 n ² - 2n - 12 = 0

Solve n:

n₁,₂ = (2 ± √(4 + 192))/8

n₁,₂ = (2 ± 14)/8

n₁ = 2

∴ n₂ = -12/8 = -3/2

So we have using n₁:

4 and 6.

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