-x2-y2-z2 minus-100-xy-yz-zx- minus-2- Find z- when x-y-3z-

Dear student, We #160;have,x2+y2+z2 100xy+yz+zx= 2 #8658;x2+y2+z2 100= 2xy+yz+zx #8658;x2+y2+z2 100= 2xy 2yz 2zx #8658;x2+y2+z2+2xy+2yz+2zx=100 #865 ...

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Standard VII

Mathematics

Types of Brackets

(x2+y2+z2 m...

Question

(x2+y2+z2−100)/(xy+yz+zx)=−2. Find z, when x+y=3z.

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Solution

Dear student,

$W e h a v e, \frac{(x^{2} + y^{2} + z^{2} - 100)}{x y + y z + z x} = - 2 \Rightarrow (x^{2} + y^{2} + z^{2} - 100) = - 2 (x y + y z + z x) \Rightarrow x^{2} + y^{2} + z^{2} - 100 = - 2 x y - 2 y z - 2 z x \Rightarrow x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 z x = 100 \Rightarrow {(x + y + z)}^{2} = 100 [u \sin g {(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a] \Rightarrow x + y + z = \sqrt{100} \Rightarrow x + y + z = 10 . . . (1) u \sin g x + y = 3 z i n (1) \Rightarrow 3 z + z = 10 \Rightarrow 4 z = 10 \Rightarrow z = \frac{10}{4} = \frac{5}{2} T h u s, t h e v a l u e o f z i s \frac{5}{2}$
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(x2+y2+z2−100)/(xy+yz+zx)=−2. Find z, when x+y=3z.

Dear student, We have,x2+y2+z2-100xy+yz+zx=-2⇒x2+y2+z2-100=-2xy+yz+zx⇒x2+y2+z2-100=-2xy-2yz-2zx⇒x2+y2+z2+2xy+2yz+2zx=100⇒x+y+z2=100 [using a+b+c2=a2+b2+c2+2ab+2bc+2ca]⇒x+y+z=100⇒x+y+z=10 ...(1)using x+y=3z in (1)⇒3z+z=10⇒4z=10⇒z=104=52Thus, the value of z is 52 Regards