Algebra - Study Mode
[#336] If $$x + frac{4}{x} - 4 = 0,$$ xa0 then the value of x 2 - 4 is equal to:
Correct Answer
(C) 0
Explanation
Solution: $$eqalign{
& x + frac{4}{x} = 4 cr
& x = 2 cr
& { ext{So, }}{x^2} - 4 = ? cr
& {x^2} - 4 = 4 - 4 = 0 cr} $$
[#337] If 4x 2 - 6x + 1 = 0, then the value of $$8{x^3} + frac{1}{{8{x^3}}}$$ xa0is:
Correct Answer
(C) 18
Explanation
Solution: $$eqalign{
& 4{x^2} - 6x + 1 = 0 cr
& 2xleft( {2x - 3 + frac{1}{{2x}}}
ight) = 0 cr
& 2x + frac{1}{{2x}} = 3 cr
& 8{x^3} + frac{1}{{8{x^3}}} = 27 - 3 imes 3 cr
& 8{x^3} + frac{1}{{8{x^3}}} = 18 cr} $$
[#338] If 999x + 888y = 1332 and 888x + 999y = 555, then the value of x + y is?
Correct Answer
(B) 1
Explanation
Solution: $$eqalign{
& 999x + 888y = 1332 cr
& underline {888x + 999y = 555} cr
& 1887left( {x + y}
ight) = 1887 cr
& Rightarrow x + y = frac{{1887}}{{1887}} cr
& Rightarrow x + y = 1 cr} $$
[#339] If a 2 + b 2 + c 2 = ab + bc + ca, then the value of $$frac{{a + c}}{b}$$xa0 is?
Correct Answer
(B) 2
Explanation
Solution: $$eqalign{
& { ext{According to the question,}} cr
& {a^2} + {b^2} + {c^2} = ab + bc + ca cr
& { ext{Put }}a = 1 cr
& b = 1 cr
& c = 1 cr
& herefore {a^2} + {b^2} + {c^2} = ab + bc + ca cr
& Rightarrow {1^2} + {1^2} + {1^2} = 1 imes 1 + 1 imes 1 + 1 imes 1 cr
& Rightarrow 1 + 1 + 1 = 1 + 1 + 1 cr
& Rightarrow 3 = 3{ ext{ }}left( {{ ext{Satisfy}}}
ight) cr
& herefore frac{{a + c}}{b} cr
& = frac{{1 + 1}}{1} cr
& = 2 cr} $$
[#340] If a + b = 1, find the value of a 3 + b 3 - ab - (a 2 - b 2 ) 2 = ?
Correct Answer
(A) 0
Explanation
Solution: $$eqalign{
& { ext{Let}} cr
& a = 0 cr
& b = 1 cr
& Rightarrow {a^3} + {b^3} - ab - {left( {{a^2} - {b^2}}
ight)^2} cr
& Rightarrow 0 + 1 - 0 - {left( {0 - 1}
ight)^2} cr
& Rightarrow 1 - 1 cr
& Rightarrow 0 cr} $$