Let the first number be = x
Let the second number which is consecutive be = x+1
As given, the product of two consecutive square numbers is 144
[tex]x^{2}*(x+1)^{2}=144[/tex]
Square rooting both sides we get
[tex]x(x+1)=12[/tex]
[tex]x^{2}+x=12[/tex]
[tex]x^{2}+x-12=0[/tex]
[tex]x(x+4)-3(x+4)=0[/tex]
[tex](x-3)(x+4)=0[/tex]
[tex]x=3[/tex] or [tex]x=-4[/tex]
Neglect the negative value so we get x=3
Hence, one number is 3 and the consecutive number is = 3+1=4
The square of the numbers are 9 and 16.
Answer:
9 and 16
Step-by-step explanation:
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