The sum of the square of two number is 233 and one number is 3 lehan twice the other number find the other number
Answers
let the first no.be x
other no.is 2x-3
so (2x-3)^2+x^2 =233
4x^2-12x+9+x^2=233
on simplifying and transposing we get
5x^2-12x-224=0
Trying to factor by splitting the middle term
1.1 Factoring 5x2-12x-224
The first term is, 5x2 its coefficient is 5 .
The middle term is, -12x its coefficient is -12 .
The last term, "the constant", is -224
Step-1 : Multiply the coefficient of the first term by the constant 5 • -224 = -1120
Step-2 : Find two factors of -1120 whose sum equals the coefficient of the middle term, which is -12 .
-1120 + 1 = -1119 -560 + 2 = -558 -280 + 4 = -276 -224 + 5 = -219 -160 + 7 = -153 -140 + 8 = -132 -112 + 10 = -102 -80 + 14 = -66 -70 + 16 = -54 -56 + 20 = -36 -40 + 28 = -12 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -40 and 28
5x2 - 40x + 28x - 224
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (x-8)
Add up the last 2 terms, pulling out common factors :
28 • (x-8)
Step-5 : Add up the four terms of step 4 :
(5x+28) • (x-8)
Which is the desired factorization
Equation at the end of step 1 : (x - 8) • (5x + 28) = 0
x=8/-28/5
2x-3=15(if x=8)or -71/5(if x=-28/5)
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